You could try the Car Park in 6 Dials just before the Criss-cross bridge heading away from the city on the Northam Road, just a short walk over the stadium access footbridge. Gosh the City Council have provided a What3words = ///canny.cloud.slime
The place we use to park on matchdays when our Girls were under 10 was Crosshouse Quay car park, almost right under the Itchen bridge, its right on the water too so that added to the diversionary amusement seeing boats and stuff whilst eating their picnic lunch, less than a 10-12 minute walk to the ground without tiddlers messing about. Bit of a chore on a full fat matchday to get away from but Saturday should be easy. what3words ///minute.museum.wisdom
Not quite as interesting and a similar walk is Bond Street over the road from the Northam Estate, marginally easier to get away after the game, if you are there in good time you could park on one of the Industrial Estate Roads for free, it is a popular spot. But an easy walk for sprouts. Bond Street is ///spring.burns.ahead
If you don't use these you know they are there for "when can we go to football again".