I did do a quick scan of the entire play, to see what the evidence was for how Jack and Lydia met, and I think it's pretty unclear. Here are the relevant facts I have found regarding how the various characters met each other. If anyone can put them all together, I will tip my hat to you:

I,i: Lydia wrote to Julia to tell her of her new romance with "Ensign Beverly". This means that Julia was not there.

III,i: Per Sir Anthony, Mrs. Malaprop and Lydia came to "our country" (meaning, whichever county is it where Sir Anthony's estate is located--I think it must be Devonshire) just before Jack was last ordered to his regiment, which I presume is not that long before the action of the play starts.

Who were Mrs. M and Lydia visiting? My best guess is that it was Julia and her father, who I am guessing, based on the surnames involved, was the brother of Jack's mother? But we don't know if that is when Jack and Lydia met.

Sir Anthony had it in his mind for a while to match Jack with Lydia. That seems to be a case of "great minds think alike".

We also know that Acres is from the same county as the Absolute family, because he is clearly an old friend of the family. And we know that Acres has followed Lydia to Bath from that same county. So I gather that Acres met Lydia during her recent visit to the country, and that is when he became enamored of her.

Bristol is mentioned several times, and I suspect that Faulkland is from there.

Julia and Faulkland got engaged about a year previously, while Julia's father was still alive. After her father died, it appears that this was when Julia began to live with Sir Anthony, her uncle. Faulkland rescued Julia on a boat, but we don't know where that body of water was. I also wonder what Faulkland's "embarrassments" are that have delayed his marrying Julia--are they financial? I am not so sure, because we are not told, as far as I can tell, that he has resolved them. Perhaps he

I,ii: Mrs. Malaprop met O'Trigger at a rout in Bath

It's also curious that Jack and O'Trigger crossed paths somewhere in Bath under such circumstances that Jack (NOT as Beverly, but as himself, because O'Trigger refers to him as a "gay captain") has offended O'Trigger enough to warrant a challenge to a duel. This is a coincidence, given that Jack and O'Trigger are both suitors for Lydia, and yet O'Trigger does not know realize that the "gay captain" is a rival for Lydia, or he would mention that.