My apologies for the potentially inflammatory question.
I have read the wikipedia article spread of islam.
The claim is made that conversion at swordpoint was rare
It is now apparent that conversion by force, while not unknown in Muslim countries, was, in fact, rare.
And that non-muslims had to pay a special tax, the Jizya
They paid a special tax; they were not supposed to wear certain colors; [...]
The wikipedia article about this tax, however, claims that
[it does] not constitute sufficient economic motive for conversion
and that it may have been smaller than another tax (the Zakat), which Muslims had to pay. (further reading suggests that maybe the Jizya had to be paid in addition to, not instead of, the Zakat)
This answer suggests that maybe social exclusion was used
those Dhimmi's have been living separate from Muslims, or were required to wear special clothes, in order to distinguish them from Muslims
but that only works after Muslims are already a majority.
It is my impression that spontaneous mass conversion is historically rare (or even non-existent). For example, places under Roman rule retained their original religions (they did not convert to the Roman religion) until the Christianisation of the Roman empire, which was imposed by force.
So if it wasn't by force, and it wasn't by economic incentives, how did the Islamic Empire incentivise conversion?