What makes the train tough is people nearby eavsdropping. Note I said tough, but not impossible. I once did a cold approach on a nice brunette honey I saw on the platform who I thought may have given me favourable eye contact. When we boarded I made sure to sit next to her.
Sadly, no positive signals, and the train is packed (peak hour), so I thought well, it's now or never. Life is not a rehearsal. So I did small talk and she responded well enough, though not enthusiastically. Kind of perfunctory. After a while she became remote, so I wound down to let my burning ears cool off (why does that always happen???). When I stopped talking there was a deathly silence because it must have been obvious I was trying to win-on. Hahaha.
So we get off, miraculously at the same stop, and she just walks away hurriedly with the crowd. No backward glance or anything. Pffft, stuff her I think and I chalk it up to experience. Anyway, the next day after work 24 hours later outside the train station, there she is sitting near the entrance by herself, seemingly waiting for me to show up. Woohoo!
What I learned from that was yes, talking on the train might be awkward for both of you, but the degree of difficulty is very high, especially during peak hour, so she may be impressed but can't show it, or there could be a delayed realisation that you are prime man meat. Who knows. You have nothing to lose except a bit of embarrasment. Nothing wrong with that if you're not a sleaze.