Certainly. The trail on the map between Warsaw and Moscow doesn't follow the actual route. That one enters Belarus more to the South.
Trains in the Baltic states are really irregular, so it might be faster to wait for the visa. The train between Poland and Lithuania only works on summer weekends nowadays, the train between Lithuania and Estonia goes only every 4 days due to some complication in Latvia, if it even reaches Estonia in an unbroken connection at all. Either way it's so impractical that you might as well forget that it even exists (as my fragmentary memory proves).
Baltic current route could be: Sat morning (weekend-only) Vilnius to Daugavpils local, to Riga local, to Valga local. Sunday morning to Tartu one modern train and then express to Tallinn. Overnight to Petersburg and finally supermodern express to Moscow by Monday noon or so.
One option, if ferries are ok, is to take the Stockholm-Riga ferry. In a few years it might also be possible to travel north around the Baltic Sea uninterrupted by train to Helsinki, and then onwards.
Trains in the Baltic states are really irregular, so it might be faster to wait for the visa. The train between Poland and Lithuania only works on summer weekends nowadays, the train between Lithuania and Estonia goes only every 4 days due to some complication in Latvia, if it even reaches Estonia in an unbroken connection at all. Either way it's so impractical that you might as well forget that it even exists (as my fragmentary memory proves).