How do you get over the hump of not being from a tech/SaaS company?

Focus on your skillsets and not the direct experience! You will often find that skills you built in your previous roles are going to be transferrable to a role in tech. Take a look at jobs you are interested in and what the posting is looking for, then you can identify how your current skills apply to their asks. Time management, organization and a team player are skills that are used in a variety of roles and skills that I am sure you have worked on in previous roles.