AWS SSO allows you to define inline policies for permission sets (Doc link). My suggestion would be to use an inline policy on that user group's SSO permission set they get assigned leveraging the
s3:ListBucket IAM action with the resource list being the buckets that you want to allow.
It's worth noting that you may need to be creative since there's a character limit (I think it's around 10k) which cannot be altered even by AWS.
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