You do , which is why it ends up being easier to attack kings in the past. Because you can't change the past, only create new timelines, attacking a king from any previous board state means that the attacking piece must be captured.

does this means that attacking the starting king position will always put the king in check of the very first board? but, he can't really escape that

Yes, but it's not that easy. Pieces still make threats according to their movement rules, whether through time or space.

For example, if your king moves from its square and an enemy rook attacks its starting position (rooks can move any number of squares in any one direction), then it's mate unless you can take the rook. However, if in the intervening time, another piece lands on the same spot, then it will block subsequent rook checks through time on that square.