Consider using the AI tool in photoshop called "super resolution". This is copied from jeffhirsch.com but you can also google it:
Super Resolution is capable of working with both Raw files (CR2, NEF, ARW, DNG, etc) and linear files (JPEG, TIFF, PSD) but typically does best when you give it a high quality Raw file to begin with. The cleaner your image is to begin with, the better it will look when enlarged. If you are starting with a JPEG that has strong artifacts, those are likely to be exaggerated as part of the enlargement process. If your source image has a fair amount of noise, I suggest running it through something like Topaz DeNoise AI first so you don't amplify the noise when you enlarge the image.
Because the Super Resolution feature is part of the Camera Raw architecture, you'll need to open your file using Camera Raw in Photoshop regardless if it is a Raw or Linear file to begin with.
Raw files are easy to open in Camera Raw and usually do so automatically. TIFF, JPEG, PSD and other linear files will require an extra step to get them open in Camera Raw.
If you are coming from Adobe Bridge with a linear files, you can Right-Click on it and choose "Open in Camera Raw" from the pop-up menu. This will bring the file directly into the Camera Raw interface in Photoshop.
Open in Camera Raw
If you aren't using Bridge and want to open the file up directly into Camera Raw within Photoshop, it takes one extra step. From the Open File dialogue in Photoshop, choose any linear file you wish to open and change the Format to "Camera Raw". This will tell the program that you wish to open the in Camera Raw even though it isn't actually Raw to begin with.
Note that you cannot open a linear file normally within Photoshop and then apply the Camera Raw filter. It must be opened up directly into Camera Raw or the Enhance feature will be unavailable.
Once you have your Raw or Linear file opened in Camera Raw, right-click on the image and choose Enhance... from the pop-up menu that appears. From there you can choose Super Resolution. (The Enhance Details option will be automatically selected when you choose Super Resolution)
Click the Enhance button and wait for the program to process your image. The task is very processor intensive. Depending on the speed of your GPU and storage, this can take a few seconds or even a minute or two to complete.
When it finishes, the program will have created an entirely separate (much larger) DNG file which will be visible on the filmstrip at the bottom of the Camera Raw window. You don't need to do anything to "save" this file as it is automatically saved to disk in the same location as the original as part of the enhancement process.
Because the file is being doubled in size both horizontally and vertically, the result is actually four times larger in overall area and megapixels.
In the case of my camera, applying the Super Resolution enhancement to a 20-megapixel original file (5272x3648) results in an 80 megapixel enlargement (10944 x 7296). And because the output file is a DNG, you can continue to edit it using the tools available in Camera Raw. The output produced by this new algorithm is remarkably free of artifacts and retains all the details of the original without getting blurry or jagged in the process. It really does end up looking like a larger version of the exact same picture. Honestly, the results of my first few tests were so clean that I wasn't sure it had even done the enlargement until I went in and looked at the pixel dimensions to confirm it really was four times larger overall.
One last tip:
Because this is an enlargement algorithm and not a sharpening one, you may also want to apply some extra sharpening after the upsampling to enhance some of the details in the enlarged image. The sharpening routines currently available in Photoshop are decent enough but a dedicated program like Topaz Sharpen AI will do even better on a job like this.