My iPhone doesn't recognize the SIM

You cannot re-activate the phone without a SIM service.

If you can get into Settings, General, ABout you may see a pending carrier update

Manually update your carrier settings on your iPhone or iPad - Apple Support

However from your description it sounds like you may have reset to factory, and without a working SIM or SIM reading components your only available optionwould be to arrange a repair

iPhone Repair - Official Apple Support

Or

 Contact - Official Apple Support

Anything other than Screen or Battery may be a replacement phone and the price is in the article under "Other damage"

See also:  Get your iPhone, iPad, or iPod touch ready for service - Apple Support

Your SIM card holder/tray might be defective (rather infrequent problem), but in order to activate an iPhone it needs a SIM card.

In such a situation, I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.