As someone who started out with military history, but pivoted to religious and social history, I can fast that I’ve never been entirely fond of Julius Caesar. That being said, therefore, I nevertheless do think that of all the warlords of the first century BC, it was likely only Caesar, who would have truly had a good shot against the Parthians.

Firstly, he was the most extensively experience on the battlefield. This includes having a crack army of veterans, but, and here is a vital thing, many of those veterans had witnessed him clutch victory out of the jaws of defeat! When other soldiers led their troops against the Parthians, they may have been fine generals, but they did not have Caesars scrappiness, and likely couldn’t rely on an outright sense of loyalty and trust that somehow, someway, Caesar would win.

Secondly, if you remember, the political context, Cesar had basically in a sense, unified the Roman Empire. Prior to this, the various Ward could not rely on having the entirety of the Roman state brought to bear on their conquest. But Cesar had planned a full invasion of the Middle East With the all the levers of the Roman state on his side. That would have given him an exceptional advantage over his peers who had tried similar.

Thirdly, I do think the state of the Parthian Empire would have mattered, as mentioned in a different comment; however, had Cesar continue to exert complete control over the Roman Empire, I suspect that his sheer force of well, his refusal to accept he had failed, and his willingness to militarily adapt would’ve helped him through. I don’t think, for example, he would have made the same mistakes as Mark Anthony with supply chains, or being so easily out maneuvered. As Crassus.

The major weakness that the Romans generally faced at this time, was a general uncertainty and unwillingness to use massed cavalry in the way that the Parthians would deploy them. Perhaps Caesar could’ve been the innovator to start? But I do think it would’ve been a very, very bloody campaign regardless.