With the qualification that this isn't my balliwick, I think it's been proven there have been matters of fraud, most notably people who no longer live in the state voting in the state notwithstanding they are no longer residents. There was even an instance of a poll worker caught on tape destroying a Trump ballot and flipping it the bird (corrective steps were taken in that case). There are also some statistical anomalies regarding the rate of which signatures in Biden heavy areas have been rejected in comparison to past elections. There is definitely some smoke there.
The legal issue is that smoke isn't enough to overturn a democratic election and the Trump campaign has been very short on proof that would show a massive conspiracy in the amounts necessary to overturn some of these margins. And when you are pursuing a lawsuit, let alone trying to overturn a democratic election, yes the burden of proof is absolutely on you. Legally, the Trump campaign would have to prove that not only was there fraud, but the fraud was in such a level that it would have overturned a democratic election. In Pennsylvania their strongest argument is that the mail in ballots were not constitutional under the PA constitution, but it's complicated, and it's a little late to be making this argument.
But that's not the only question. The other question is do Republican voters believe the election was stolen and a surprising number of them do. And it's not just the legal stealing which counts in this question but the thumb which several people have put on the scales such as: the Russia investigation, the impeachment, the press bias (including during debate moderation), the position taken by big tech, the mass mail in ballots, and now the allegations of cheating (even if that cheating, such as restricting poll monitors from observing, didn't in fact change the outcome of the election). It sets up a situation where the narrative from here from Trump is that the election was stolen, and a large part of the Republican base will believe it. Add to this that Biden seems reluctant to publicly go against his experts (even the ones on his taskforce calling for a lockdown) and seems to be reinstalling a lot of Obama admin people in the admin (as opposed to Sanders/Warrens rebels, and which will be characterized by Rs as the swamp coming back).
More concerning, the polls showed a large number of D voters doubted the legitimacy of the 2016 elections. Build in 2000 to that and you have a situation rapidly developing where neither party will believe in the veracity of elections and will be determined to do whatever it takes to put a thumb on the scale for the next one. It's not a good situation for a republic when election integrity begins to disintegrate.