Is it normal to use ‘the second’ without a preposition in expressing ‘as soon as” or ‘no later than’?

Solution 1:

Using "the second it was available" is hyperbole. The normal way of expressing that is "as soon as it was (made) available". You can replace "second" with "instant" or "minute" to maintain the hyperbole. "The second" looks like an adverbial phrase of time, just as "as soon as" is an adverbial phrase of time.

You could change "the second" to "at the very {second/moment/instant/minute} it appeared" if you wanted to use a prepositional phrase, but it's not necessary.