Have you tried joining social meetups? Not to look for dates. Generally speaking, that's frowned upon. Or at least the meetups I have attended.
Try joining meetups that cater to person's on the spectrum or meetups that cater to introverts and people with social anxiety. Hopefully, the ones in your area are hosted/led by competent individuals who can help keep the meetups lively but to whatever level of social engagement you feel comfortable at.
Alternatively, maybe there are dating apps that are specialized for individuals on the autism spectrum. But I would think that might be too much pressure on yourself until you have more confidence in your own social ability.
Consider attending the above social meetups as exercising and workouts ... but for your conversational and social skills.