I'd say the number one thing to do when you're transitioning into a new industry is to try to get an internship (applying directly and via dm). Also try to get people who will vouch for you (networking via coffee chats, events, Slack communities, etc.)
The tricky thing about moving into SaaS is the homework you need to do. People assume you have a baseline knowledge of the players in the space, the tech, and core concepts.
For entry level positions, people care more about you showing initiative and being curious rather than your concrete work experience
