Hi,
GTIN and/or MPN can indeed be required by Google merchant.
The HikaShop Google Products plugin actually has options to provide them to Google.
For example, the "Add Product Code (mpn)" setting of the plugin will use the product code you entered in your products as MPN in your feed.
And you can use the GTIN setting below to add the GTIN.
I would recommend to have a look at all the settings available in the plugin and their tooltips.
And you can also read the Google merchant documentation which explains what is needed for which type of products:
support.google.com/merchants/answer/160161?hl=en
It's all explained in there.