This was not in origin a bare infinitive so much as it was a present subjunctive form under subjunctive inversion. The key to understanding what’s happening here is the inversion; that is, that the subject follows the verb. You may also notice how the verb is not inflected to match the subject; it is always the unmarked form of the verb such as we use in infinitive and commands.
Even though this construction is mostly no longer productive in present-day English, at least with other verbs, it does still occur with reasonable frequency with the verb come. Put the base form of the verb first followed by the subject:
- Come Saturday morning, I’m going away with a friend.
Meaning: Once Saturday morning gets here, I’m going away with a friend.
- Come tomorrow, you’ll find no rats left in this town.
Meaning: As soon as tomorrow gets here, you’ll find no rats left in this town.
- Come rain or come shine, the mail always gets through.
Meaning: No matter whether the rain comes or "the shine comes", the mail always gets through.
You can find plenty of “recent” examples of this:
- But come the next session of Congress, State can expect only that its summer guest will bite its hand when it goes to the Capitol asking money for diplomatic entertaining expenses abroad or for living expenses for its diplomats.
- But we can handle them come the time.
- Come the turn of the year, Rush will be chasing yet another landmark – Denis Law’s record of 41 FA Cup goals.
- If not, the lessons are clear – there will not be a kick-start come the next election, but the Tories will be kicked out.
We really don’t do this very much (if at all) with any verbs beyond come alone. Because of this now-special case that isn’t generalizable to other verbs any longer,
Huddleston and Pullum have decided that modern speakers have synchronically re-analysed this come construct — which diachronically was without question a subjunctive form — as a preposition(❗) that takes a time expression as its complement. You can read more about this in Tim Waller’s 2017 PhD thesis for University College London, “The subjunctive in Present-Day English”.
But given how H&P seem to treat everything as a preposition, I’d take that with a grain of salt if I were you. :) If you do want to think of it as a preposition, it becomes a synonym of by + time expression.
You may be more used to seeing a sentence starting with what otherwise looks just like a bare infinitive when it occurs in conditionals, although this can be analysed as an instance of conversational deletion rather than as subjunctive inversion:
- Ask me no questions, I’ll tell you me no lies.
Meaning: If you ask me no questions, I’ll tell you no likes.
- Take one more step and I’ll blow your head off.
Meaning: If you take one more step, I’ll blow your head off.
You’re probably more used to subjunctive inversion like this in unreal conditionals:
- Were there any other route, we would have taken it.
Meaning: If there were any other route, we would have taken it.
- Had we only known what was in the box, we would never have opened it.
Meaning: If we had only known what was in the box, we would never have opened it.