Create a custom forgot password flow for your users.
If neither of these options will work for you, or if you want more control of your user's experience, it's possible to create a completely custom Forgot Password flow using lower-level methods.
First, make sure you have Email verification link toggled on for your application. This can be found under the Authentication factors section of the Dashboard.
You can also achieve a similar result by sending a One-Time Password with an email address. Simply pass the value email_code as the first-factor strategy. Just make sure you've collected the user's email address first. You can find all available methods on the SignIn object documentation.