How Do I Get the Correct Date Into My Google Takeout Photos?
The real dates are in the .json files next to your photos. Here is the easy way to write them back into the pictures, without the command line.
The correct date is already in your export. It is in the .json file sitting next to each photo, in a field called photoTakenTime. Your problem is that no photo viewer reads those files. They read EXIF, which is the block of information stored inside the image itself, and Google left that part empty.
So the fix is a copy job: read the date out of each .json, write it into the matching photo, and set the file's own timestamps to match. Do it for one photo and it takes a minute. Do it for forty thousand and you need software. You can write an exiftool command, and plenty of people do, but the sidecar filenames make it fiddly: Google cuts long ones off partway, uses two different naming styles depending on the year, and puts the (1) counter in an odd place on duplicates. A pattern that misses those quietly skips files.
The app handles all of that for you. Choose your Takeout folder, choose where the fixed photos go, and press start. It matches every sidecar to its photo, writes the date, time and GPS, and tells you at the end which files had no data to work with. Nothing is uploaded, and the first 500 photos cost nothing.