It's a bit late in the day - or would have been for me when mine were little - but there's one at Polwarth Church on a Thursday afternoon. Details here although there's also something about a Tuesday morning so worth giving them a call/walking past to check.
Google ‘buggy walks’ or find this on meet up app. I’ve found this a great way to meet other mums. We meet up, go for a walk then head to a child friendly cafe. It’s free, you don’t have to commit to going every week and I just love getting out in the fresh air. There are walks all over the city on different days and at different times. Hope you find something that suits you, so important to get out of the house.