The answer is:
A pawn in chess!
I live my life on the top floor,
They are found on the second row of the chess board above the major pieces
Yet still aiming to get from where I am to something more,
Reach the top row to become a queen
An upgrade if you will,
become a queen
Just by climbing the hill,
moving upwards
For glory to my possessor!
to win the game
I usually take baby steps after a big stride,
moving one square forward at a time after pushing two squares forward.
Part of a long chain I often abide,
usually found in a pawn chain
I often need my companions support,
other pawns that support, part of a chain, or other pieces
Yet alone I can become to close for comfort,
With a little shove!
It can attack enemies’ pieces with a push.
Title
Pawns cannot move backwards
What am I?
A Chess pawn