I think in countries within the relevant WTO treaty even as a small business your mark can theoretically recieve a "well known" status and similar protection as if it were registered. But no idea how well this works, and in practise I reckon you'd still want to register trough the Madrid system for the regions you plan to do business in directly
The question is, what does "doing business directly" means. You have a website / a SaaS product, and then people from all around the world can subscribe. ¯\_(ツ)_/¯
If you start doing business is a country using a name it (usually - depending on local laws) provides some protection against others registering that trademark in that name (as a non-registered trademark).
You need documentary evidence you were using it in that country before the trademark was attempted.
You can then spend the money to register a trademark at some future time.
But talk to a (good, IP specialist) lawyer! Even $5-$10K on lawyer fees is cheap compared to registering international trademarks in multiple categories.