As to why I'm inclined to posit an omitted of, it's simply because positing an omitted preposition makes the construction easy to parse and not very anomalous
Yes, I see what you mean. Positing a missing preposition I agree helps make sense of things to some extent even though it's not there structurally. I imagine this 'of' may be a ghost of a former historical incarnation that has all but faded away, possibly a vestige from the pre-modern era of English and lingering on diachronically in places thereafter.
Compare my first time talking with him with my first experience interacting with him: That was my first experience interacting with him. Of comes out of hiding in the paraphrase That was the first experience I had had of interacting with him.
The -
ing form, as opposed to an infinitive form, suggests a focus on a particular
experience by the subject, which is why the word 'experience' works apparently synonymously with 'time' in many cases:
It was my first time driving a tractor.
It was my first experience driving a tractor.
Interestingly, however, with different structure, the mismatch in meaning is revealed.
It was the first time I had driven a tractor.
It was the first experience I had driven a tractor.
This tells me that the sense of there being a personal experience comes from the possessive word 'my' along with the present participle form of the complement participle clause. Also, that the word 'time' denotes the particular occasion at which the personal experience happens and that words that fit in this slot represent a small and closed class.
So an initial question that I would ask is what exactly this pattern is in its broadest but most precise formulation. At the moment I have it as this:
posessive determiner + restrictive modifier + 'time' + -ing clause
Additional questions:
Which other words can replace 'time'?
Must the pattern include a possessive determiner?
How large is the set of words that can fit in what I'm calling the 'restrictive' modifier slot?
Is the 'restrictive' modifier part crucial to the pattern? If so, how? Do we get a different pattern without it?