I want to create a world full of different civilisations and I want one in a desert but how would I make it believeable.
No particular problems in making it believable. You can take as reference the cultures which developed on our planet and in our deserts, like
- Tuareg (for warm desert)
a large Berber ethnic confederation. They principally inhabit the Sahara desert, in a vast area stretching from far southwestern Libya to southern Algeria, Niger, Mali and Burkina Faso. Traditionally nomadic pastoralists, small groups of Tuareg are also found in northern Nigeria
- Sami (for cold desert)
an indigenous Finno-Ugric people inhabiting the Arctic area of Sápmi, which today encompasses parts of far northern Norway, Sweden, Finland, and the Kola Peninsula of Russia.
There are many more all along the history, so based on your world level and climate you can choose what suits best your needs.
Two alternatives I can think of:
They could have started as river folk, living in a small habitable zone next to a river flowing through a desert. Basically, they are living in the zone that floods yearly.
Then they could have expanded by irrigating. They would not be able to expand much past the distance from the river that they could effectively irrigate. That would encourage them to invent canals and dams and reservoirs and such. Maybe they learn to store water in sand-filled basins then pump it back out of wells. That reduces evaporation quite a bit, at the expense of needing to do a LOT more work at pumping.
But realistically, they probably can't go a lot more than about 50 km either side of the river. If the river is long enough, that could still be a very large empire. Belgium is about 30,000 km^2. So if this river was 300 km long they could have an area equivalent to Belgium.
Though it would have to start out as a quite wide river. Otherwise, they'd use it all up in irrigation. They would need to save a lot of water in the spring floods.
2) They are in a trade bottle-neck of some kind.
This assumes there are at least two other civilizations that want to trade through this desert.
Imagine they have a city that sits on the only source of drinkable water for a long distance. Maybe a river goes north-south through the desert, and the only sensible trade route is east-west through the desert. Or imagine their desert is on a long narrow chunk of land between two oceans and that contains the only land trade route. And they have a nice lake fed by glaciers on the only mountain in that neighborhood. Or imagine there is alkali water and they have developed a technology that lets them purify it enough to drink. They are the only water on a trade route.
They can extract tribute from every caravan. This will encourage them to develop proficiency with weapons to keep the traders from trying to cheat. And that will encourage them to get up to lots of other things. Why should we be satisfied with keeping this gateway out here in the desert? We should go smack them around in their fat, water soaked cities, and be kings over there.