please entertain my crazy mind lol

okay, so we're not officially trying for a baby. but.... I'm crazy excited and am really hoping we get lucky early lol. so, my LH was almost positive at 8pm on Wednesday, and by Thursday morning (I didn't use the first urine) was definitely positive. so since we aren't officially trying, he is still cautious around my fertile days. Monday night he didn't seem to care to much and did not withdraw when he ejaculated. I'm sitting here trying to not let myself go crazy wondering if there's a chance or if it's too far out. I assume I'll ovulate anywhere from today (did have some cramping and nausea) to tomorrow. Am I getting my hopes up or do you think there's a decent chance we could conceive? If I ovulate today that would mean the sperm would have had to lives 3 days and tomorrow would mean 4. has anyone else had an experience like this and gotten a BFP?