There are 2 ways to do this
1) Using PHP. Doing it with PHP would mean that you’d need to update the post to load the alt text and then update a second time.
You would use an acf/prepare_field (https://www.advancedcustomfields.com/resources/acf-prepare_field/) or acf/load_value (https://www.advancedcustomfields.com/resources/acf-load_value/) filter. In this filter you would get the image field, get the image alt tag and set the field value.
2) The second way is using custom JS and AJAX. This is more complex, but probably what you’re looking for.
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