I think that after c5, a cool idea would be to play b4 immediately with the idea of taking on c4 and opening up the Queenside. Long-term ideas of developing the Queenside pieces and and developing an attack against Black's king with a fiachetto'd dark square bishop.
After 3...c5 both 4.g3 and 4.c4 are found played almost equally in databases. Each leads to a different type of game. We considered 4.b4 in this game but went with 4.g3 almost arbitrarily, simply because the last time we saw this position we had played 4.b4. Then we never did play b4 due to the Nc6; something to keep in mind next time we see this position.
You can see that discussion [Here].
VC Analysis - Little Big Pawn
https://www.chess.com/votechess/game/130544
Stockfish 10 depth 20