Network as Bud Fox did it ?

Hi,

the people who don't know who Bud Fox is should read this paragraph:
He is one of the main characters in the movie "Wall Street (1987)".
In the beginning of the movie he is working in a bank as a trader.
But he is not happy with that job, he wants to become an Investment banker.
What he does to become one: He puts a lot of effort into getting the chance to talk to the CEO of a great Investment firm. His objective in this talk: Getting hired by the CEO. And that is also what happens.

What I did has similarities to Bud Fox. I have put a lot of effort into getting a chance to
talk to CEO's and I became some chances.
What is different: My objective was not to get hired, since that would be to early right now (people told me because of my lack of internships I have to start with lower jobs as in the Big 5 companies), I wanted to establish a contact, that I could reach out in some months/years and then do the Bud Fox style and force to getting hired.

What do you guys think of this strategy? Should I continue to do it? (Which means long term investment)
Or should I focus on networking with the relevant people who could hire me right now (which means Big 4) ? Experience of somebody would be of great help.

Sincerely,
Kai