OAI has certainly positioned themselves culturally the same way as Google did for search engines. Google this, Tweet that, ask ChatGPT.
We know now how much actual competition[0] Google had after the dust had settled, in all practical terms - zero. Even after all the SEO spam and enshittification they haven't lost any notable market lead.
Time will tell if ChatGPT ends up that way but unless OAI implodes (which isn't all that unlikely) they're on the way there.
But Google came years late. I used multiple search engines before Google finally emerged as a winner. altavista, excite, hotbot and others; there was a huge hype around the Lycos IPO and then alltheweb was a thing for a time and then Google won.
So being first does not necessarily mean winning.
And Twitter had strong network effects.