Unfortunately, as mentioned by @diegolippel, you will have to keep track of subscription next charge dates in your own application and trigger a billing attempt.
@HD_WORK be very careful when building this and make sure you use idempotency tokens. The contract will also let you create a billing attempt on a SubscriptionContract even if its not "due" yet (which means the next billing date is just a value store). There are no guardrails other than the idempotency token so you will need to build your own.
I would love to hear from Shopify why this is the case as it does not work like any other subscription API out there (Stripe, etc). I would imagine that end customers would trust Shopify to bill them as per the "Subscription Contract" which turns out to not be a contract whatsoever.