Under U.S. law, there is a very limited time period for challenging the results of an election.
For president, there are three relevant deadlines (two of which are almost simultaneous). First, for a judicial challenge under state law, such a challenge must be resolved at least six days prior to the meetings of that state's electors. As electors meet on the Monday immediately after the Second Wednesday in December, the deadline for resolving a judicial challenge to the state's results is the day before the Second Wednesday in December. Second, when Congress meets to count the votes on January 6, members of Congress can challenge the validity of the certificate of votes in a given state. Third, in theory, Congress could also consider a challenge to the count of those votes (i.e. that the numbers have been added up wrong). However, once Congress has officially declared the results of the vote of the electoral college, there is no further mechanism to challenge the winner.
In any case, the Ukraine story has nothing to do with the 2016 election but rather involves another potential ground for impeachment (a potential misuse of presidential power by tying foreign aid to a foreign government reopening an investigation into one of the President's domestic opponents). If President Trump is impeached and convicted, there would be no "do over" of the 2016 campaign. Instead, Vice-President Pence would become president.