Yes, you can fix your Mac's port to deal with your MacBook Air not recognizing your USB hub issue. But before checking your Mac's port, let's try some simple solutions first.
As you mentioned in the post, your USB hub cannot be recognized by your MacBook Air at all even if you have changed it to another one.
In such a case, I always recommend you check the USB hub. You can connect the USB hub to another computer, and then connect your mouse and SD card to it to see if your test computer can recognize it. If it cannot, then it's your USB hub's problem. If your test device can, then it's your Mac's problem.
Facing a USB hub problem, you can choose a better-quality USB port adapter or SD card adapter for Mac alternatively.
You can try to restart your Mac to fix your MacBook Air won't recognize the USB hub problem. Click the Apple Menu on the upper left corner of your Mac screen > select the Restart option > then the Mac will shut down and restart automatically. After this action, you can try to insert your mouse and SD card again to see if the Finder on Mac will pop up a notification.
If the restart operation doesn't save you from the troublesome condition. Try to update your Mac's USB driver. When your USB device is not detected by Mac, you should check to see if any USB driver updates are available. Click on the Apple in the upper left corner of the screen > Select "Software Update...".
Any available updates will be listed in the Software Update main window, and you can also tick the Automatically keep my Mac up to date option to make your USB driver always renewed.
Finally, the physical problem of Mac port can cause your USB hub not to work on your MacBook Air. If all mentioned approaches above cannot deal with your Mac not recognizing your USB port issue, head to the local Apple center for the professional repair.
Read more: Fix USB Flash Drive not Showing up on Mac