You can use any Distance Matrix API for these. For example, Distancematrix.ai. It has a free pricing plan, so may fit your needs better.
To start using the API, fill in a form here https://distancematrix.ai/contact, and you will instantly get a letter to your email with your token and detailed information on how to use it.
During a 7-days trial period, you have the full unlimited access to Distance Matrix API and the opportunity to test it. When the trial period expires, you can continue using it for free, or you can switch to another pricing plan.
Besides, if you were using Google's API before the migration for you will be easy, because you don't need to rewrite code. You can compare the requests here:
Google:
https://maps.googleapis.com/maps/api/distancematrix/json?origins=<origin_location_1|origin_location_2|...|origin_location_n>&destinations=<destination_location_1|destination_location_2|...|destination_location_n>&key=<your_access_token>
Distancematrix.ai:
https://api.distancematrix.ai/maps/api/distancematrix/json?origins=<origin_location_1|origin_location_2|...|origin_location_n>&destinations=<destination_location_1|destination_location_2|...|destination_location_n>&key=<your_access_token>
If you need a customizable solution or have some questions before you start, just feel free to respond to the letter you will get after filling out the form.
Disclaimer: I work at a company that creates this API.