I have some domain knowledge here, as I used to (identity unmasking potential) be involved in the WinFax product development group. Ancient history now, but a lot of that facsimile via telephony knowledge cruft is still embedded in my head, albeit rather fuzzily.

My advice would be to source out an online fax service that supports email-to-fax or some sort of 'upload document to the service and we fax it out'. There used to be any number of companies in this space, and I suspect some of them still exist as forgotten offerings within a much larger company. Even some of the large US telephone companies offered their own PC-to-FAX delivery services.

Some of them made money on fees for inbound faxes (since you needed to pay for a phone number (not an actual phone line, just the fax number)). They would receive faxes at 'your' number, then email them to your inbox, with per page, per month, or whatever fee structure. The outbound faxes from the customer were sometimes included/free, especially for destination numbers within the US.

Since inbound fax volumes (as routed through these services) for many people have greatly dwindled in recent years the fax service fees have expanded to charge more for outbound. But, the actual cost to dial a fax machine from a computerized server is still tiny, fractions of a cent per minute.