Can't you just add silence to the start?
Yes, I guess I could do that also, but either way now the two recordings won't be the same length which gives me another issue to deal with.
As others above have noted, you're not trying to get the two recordings to be the same length; you're trying to get them to align throughout the course of the music, which is slightly different.
My workflow, which I've been following for a mind-numbing number of Merge festival tracks now, is:
1) Import both tracks into Audacity.
2) Trim the start of one track or add silence to the other until the first big spike of amplitude aligns. (I do this visually while zoomed in by an extreme amount, then check to hear that it sounds okay, which it always does.)
3) Scroll to near the end of the recordings, and find a clear loud fast-attack spike (snare drum hit is usually good) in both recordings.
4) Click on the spike in one recording, change the Selection display to "Samples," then copy down the number.
5) Click on the same place in the spike in the other recording, and drag to select everything between there and the start of the recording.
6) Effect > Pitch and Tempo > Change Speed and Pitch, then type the number from step 4 into "New Length."
Done. There will be a teeny amount of drift in any part of the recording after that late spike, but it won't be enough to be noticeable over the few minutes left to run at that point.