QuickSight does not allow the ability to pick which date options you may present to your users. If you’d like to only allow your users to select year and month, you would need to create separate string parameters that link up to your date field with calc. fields.
I will mark this as a feature request for additional date filtering options to promote visibility to the support team.
Since we have not heard back, I’ll go ahead and close out this topic. However, if you have any additional questions, feel free to create a new post in the community.