Need some Advice on getting traction with marketing roles on larger companies.

I am growth marketing professional (8+ years) and most recent was Head of Marketing at a venture back startup. Quick career progression - Did banking for 3 years -> joined a marketing agency as a performance marketer and worked up the ranks from analyst to vp in 4 years -> was marketing hire number 1 at a venture back startup as director of marketing for 1.6 years (Series A to C) -> was the same title and level at next startup (Series A to B) -> laid off a few months back. I am trying to break into marketing a bigger companies like Pepsi, Booking.com, Credit Karma etc. How do I go about networking to market myself as a candidate to these companies? For venture startups I was just either introduced, had a headhunter recruit or it was easy to find roles on Linkedin. I have a tough time figuring out how to build conversations/ leads for these roles. Thanks for any advice, I appreciate it.