It doesn't look like this is currently possible, which is interesting considering you can filter based on the customer creation date within the Shopify admin. I'm not sure of the reasoning behind that, but it strikes me as more of an oversight than an intentional decision. I'll report this internally in hopes we can get that added for you!
Good news - this actually is possible after all. The query value is just named differently when setting it with the API.
You can pass "query": "customer_date:last_month" when creating a CustomerSavedSearch for example, and that'd give you only customers created within the past month.
You can also pass the following: last_week, past_week, last_month, past_month, last_3_months, past_quarter, last_year, past_year. Dates in the format of 'yyyy-mm-dd' also look like they work with < and > symbols before them if required.