To fix the MMS won't send issues on Samsung Galaxy devices, first, ensure that Mobile Data or Wi-Fi is enabled and you have a stable internet connection.
Next, clear your messaging app's cache and data, then verify and update your APN settings according to your carrier's specifications.
Consider using an alternative messaging app, such as Google Messages, to pinpoint potential issues with the default app.
Lastly, contact your carrier's support center for assistance, and perform a factory reset only as a final solution.