You can not assign random data. All product identifiers need to be 100% correct.
If you don’t have a valid bar code or MPN assigned by the manufacturer, then do not use it. And set your products to be custom.
If you do not follow Google Shopping guidelines, your product ranking will drop and your performance will lower.
If you need more specific control of your data feed, have a look here: https://feedarmy.com/shopify-google-shopping-feed/