I was in a similar position when I started in social media marketing. Since I didn't have much experience, I created sample content and put everything into a Google Drive portfolio that I could share with potential clients.
When applying, I'd even create a few free sample posts specifically for their brand to show what I could do. For a couple of clients, I offered to manage their social media for free for 1-2 months in exchange for testimonials and real results. Those free projects helped me build a portfolio, and eventually I landed my first paid client.
Just make sure you're using free work strategically to build credibility, not doing it indefinitely.