Did you see the physical SSD when you followed @leroydouglas' instructions?
If the physical SSD is seen and First Aid doesn't show any errors (especially when manually looking through the report) yet the installer still does not allow you to choose the "Macintosh HD" volume (default name unless you changed it), then you have one of these issues:
- SSD has Filevault enabled, but you did not unlock the volume as I mentioned in my other post
- SSD has Filevault enabled, but Disk Utility would not unlock the volume (requires a clean install by first erasing the SSD -- all daa will be lost if you don't have a backup)
- There may be a partition or filesystem issue which requires a clean install by first erasing the SSD -- all daa will be lost if you don't have a backup
If the physical SSD is not seen, then the SSD has most likely failed requiring you to have Apple or an AASP examine the laptop to provide you with a repair estimate. You will most likely lose your data if you don't have a backup, but you could have a professional data recovery service attempt to recover data from the SSD.
At this point the only thing that matters is whether Disk Utility can see the physical SSD. If so what are the results of First Aid when following the instructions provided by @leroydouglas? And is Filevault enabled?