Can you cast Polymerization on your first turn?
Yep, you can actually do that given you had the cards. Do note that some cards may have other restrictions that may prevent you from doing that, so make sure to be aware of such possible restrictions.

Compared to MTG, Yugioh is quite faster. It is not rare to see First Turn Kills (FTK) on top tier decks, or well One Turn Kills (OTK, basically same as FTK but not on first turn, just 8000+ damage in one turn) on any tier deck.

This is part of the Yugioh game format and strategy, as it is designed for "faster" duels. This is one of the reasons why in championships players compete by Match, which is a Best of Three sequence of games. This is also, perhaps, why one mistake in Yugioh can be more harmful than one mistake on other TCGs, so be sure to watch out for these sort of moves that can wipe you out in an instant.