Question about booking small gigs for a new indie punk band

My band just put together a set of original indie punk songs and we're itching to play live. We've hit up a few local spots but keep getting ghosted or told they're booked solid. How do you guys get your foot in the door with venue bookers? We're based in a mid-sized city with a decent scene. Should we try opening for other bands first or just keep spamming demos? Any advice on making our email stand out would be huge.