While Dragon Ball's Goku has proven himself a warrior time and time again - one mighty enough to go head to head with gods - would he be able to lift Thor's hammer? The answer is yes, but it's not a simple conclusion to reach. Mjolnir can only be lifted by those worthy to wield it, but that enchantment has taken on a life of its own. Originally cast by Odin, but maturing over time and influenced by the Mother Storm within Thor's weapon, Marvel Comics has never fully committed to exactly what being "worthy" means - so how can anyone be sure Goku qualifies?
The Saiyan warrior will likely never get a chance to wield Mjolnir (though it's not impossible, as the Avengers have seen weirder crossovers, like when they fought the titular monsters from Attack on Titan), and yet if he did, it's a safe bet he'd be able to live up to the conditions required to lift it. Not, of course, by merit of sheer power, but because of a laundry list of qualities that make him way more similar to Thor than many suspect.
What makes someone worthy?
The MCU has already established that elevators aren't worthy, and that tricks of moving the hammer without wielding it don't count. What matters is a person - or android's - character, though this can change, since Thor has had moments where he's lost his worthiness, thereby losing his ability to wield Mjolnir. In Original Sin, Thor loses the ability to wield Mjolnir when Nick Fury convinces him that humans are better off without gods, robbing Thor of his sense of purpose.
Thor's original stories imply that a degree of humility is necessary to wield Mjolnir, but so is some degree of accomplishment. It's through the feats of his youth that Thor gradually becomes worthy, finding the hammer less and less heavy as he's aided and abetted in his adventures by the shifting loyalties of Loki. Evil characters, even those convinced of their righteousness, have been unable to wield Mjolnir, making it clear the hammer must be raised out of some desire to help or protect others. It's also clear that to wield the hammer, a hero must judge themselves worthy to do so. It's likely because of this that when people other than Thor have been able to pick up Mjolnir, it has been in moments of dire need.
Who has proved themselves worthy?
Wielders of Mjolnir have included Beta Ray Bill, Jane Foster, and even Eddie Brock. However, each of them took up the weapon in a moment of desperation, whether it was Brock standing against the King in Black or Jane Foster defying her cancer to give Earth the protection it deserved when Thor was unworthy. The largest assemblage of Thors ever occurred during the Secret Wars event, when a godlike Doctor Doom commanded a legion of Thors from different realities. In this situation, the Thors weren't desperate, but they were assured of their righteousness in serving a higher power, suggesting that it's not desperation that allows mortals to lift the hammer, but true faith in the task before them.
However, there are also some wielders who are not part of the Marvel universe. DC's Superman once lifted Mjolnir in a moment of desperation during the JLA/Avengers crossover. The same is true of Wonder Woman. This would mean that a defining characteristic of lifting Mjolnir does not include being a Marvel character. Adding in the others who have lifted Thor's hammer also makes it clear you don't have to be a god or even human to lift Mjolnir. Beta Ray Bill is a cyborg Korbinite - as alien to Thor as a Saiyan like Goku.
What about Goku?
Like Superman, Goku is an alien from another planet who was raised on Earth. He adopts Earth as his home and he has defended it numerous times. Like Thor, Goku is also based on mythology, inspired by the legend of the Monkey King. While the Monkey King's story is very different from Thor's, both have mythological backgrounds with godlike abilities as a result. In terms of godlike power, Goku and Thor are definitely alike. Godhood isn't a requirement to lift the hammer, but it definitely helps with the core characteristic of extreme faith in one's right to wield the weapon and the warrior mindset which Mjolnir seems to prefer.
One argument that fans might use against Goku is his tendency to recklessly endanger others and be selfish in that framework. After all, he did remind Zeno of the Tournament of Power - which literally had the aim of figuring out which worlds should be destroyed since they're too weak to save themselves. This was all because he was eager about a fighting competition. So there have been moments when Goku has made some questionable decisions. Yet Thor has also made questionable decisions without becoming unworthy - at one point considering abandoning humanity - and even when he's lost worthiness, he's gained it back by becoming a better person, and thereby a better god. In a moment like this with the Tournament of Power, Goku certainly would not be worthy, because he would be putting his own selfish desires ahead of the safety of others. While this point could be argued against Goku's character, he has far more moments where he puts his life on the line to save others. These are the moments that would make him worthy.
Goku has plenty of moments where he risks himself for the greater good without hesitation, and as Earth's protector, he fulfills a similar role to Thor in Marvel Comics. He also wouldn't struggle with the idea of being unworthy of Mjolnir's power. The Super Saiyan is always trying to build up more power, and he is continuously one-upping the best fighters around. Goku has trained with gods and gained godly powers himself without hesitation.
Goku has the godly confidence - bordering on arrogance - and warrior's spirit that allows heroes to lift Mjolnir, but is he free enough of corruption and self-interest to do so? A major clue that this is the case is his ability to ride the Flying Nimbus in Dragon Ball, Dragon Ball Z, and Dragon Ball Super. The main requirement of riding this magic cloud is to be pure of heart. Goku may be a child when he initially rides it, but he's an adult in Dragon Ball Z, capable of riding it nonetheless. Flying Nimbus largely disappears after Goku gains the ability to fly, making it unnecessary to use the cloud, but he abandons it out of practicality, not because he has become unworthy.
Goku Could Lift Mjolnir
In moments where Goku remains pure of heart, selfless, and when he commits to the higher duty of protecting those who need his help, he should be able to lift Mjolnir. Goku has had moments of selfishness, but so has Thor, and gods are inherently more self-centered individuals. Looking back over Thor's comic history, he's been just as impetuous and arrogant as Goku without becoming unworthy. Furthermore, characters like Jane Foster and Beta Ray Bill rule out some of Thor's more divine qualities as prerequisites for hurling his hammer. In a situation where he was fighting a terrible enemy and needed Mjolnir to defeat them, Goku should absolutely be able to lift the hammer. The real question is whether he would.
Goku used to use a magical staff in battle, but after a while he focused more on martial arts and now often uses his Ki abilities more than anything else. He seems to largely prefer hand to hand and Spirit Energy based combat, so choosing to use a weapon against a foe would be out of character for him. So, while Dragon Ball's Goku could lift Thor's hammer, Mjolnir, the same nobility and fighting spirit that make him worthy would likely mean he'd instead focus on pushing his limits and find a way to win without it.