Usually an invoice as such is not necessary. A SOL would run from the time the service is performed or the goods are transferred. And the vendor could sue, after that time, without an invoice or other additional notice. An invoice is merely a courtesy in most cases.
I'm not sure, but it appears from reading
this that the SOL is 2 years.
Seems awfully short, IMO, but whatever.
I'm assuming that the OP as well as the vendor are in Ontario. If one of the parties is in another jurisdiction, the SOL for that jurisdiction might apply instead (were the vendor to sue in that jurisdiction).