Can I issue invoices without a VAT number if I work as a freelancer?

No, technically you can't issue proper invoices without a VAT number. An invoice is a tax document that must contain the VAT number of the person issuing it, and it's mandatory for transactions between professionals and businesses. If you work as a freelancer and haven't opened a VAT number, what you can do is issue a "receipt" or a "payment document," but that's not a real invoice. Many clients accept this solution though, especially if it's occasional work.

That said, if you work regularly as a freelancer and earn more than a certain threshold (the threshold varies but it's low), you're required to open a VAT number and keep records. It's a hassle, I know, but getting caught unprepared by the tax authority is much worse. Opening a VAT number isn't complicated - you can do it online in a few days. Once you've got it, you'll be able to issue proper invoices and have everything in order.

If your work is really sporadic or occasional, talk to an accountant before you decide; maybe there's a simplified regime that works for you, or you can legitimately stay under the threshold. But the advice is don't risk it with fake invoices or made-up receipts: the consequences are serious and it's not worth it.