The e-mail offers are not random. They come when Business loads are exceptionally light, or (more often) when Economy reaches capacity and there are still seats in Business, they try and squeeze out a bit more revenue before making op-ups.

If you manage your booking via either the app or the website you should see options to upgrade to Business. The only reason you would not see them is if Business is full already, or you have bought a “special” fare type ticket.

You can also updgrade at check-in. Skywards members also have the ability to upgrade on the plane (which can avoid taxes if you are departing from a country that imposes them such as the UK).
Again, all subject to availability.

If you’re not a regular Business traveler, be prepared for a heafty price tag, the upgrade will typically cost 5-10 times the cost of an Economy ticket, but also if you’re new to Emirates Business is 5 - 10 times better than Economy so it kind of works out.