>>23332538They kinda got rid of the baby mechanic during the Ruby/Sapphire era. There were some cards with a Poké-Power that would let them evolve, then some cards that couldn't evolve but couldn't be hit while asleep, and right now I think there's no "baby" Pokémon at all in Standard format.
Pic is the closest I can think to a basic having a similar effect, but keep in mind current rules state you can't attack on your first turn if you go first. However, if you win the coin flip at the start of the game you get to choose who goes first.