Not necessarily too late, but you need to get started IMMEDIATELY.
LCA takes seven days - cutting it very close here. Would need to be in USCIS' hands before OPT expires to go to DSO and get cap-gap endorsement; grace period won't work.
Speak to a lawyer fast.
As of April 9, USCIS has only received 17000 (approx applications) so it is not too late. Lca's are taking 7 days for approval. The LCA can be posted at the time of filing. You did not need to post before filing. You will be able to work in the cap gap period