Typical? Villages and towns or cities serve fundamentally different functions, and most of the time it makes little sense to convert a perfectly functional village into a town. Towns and cities are geared towards commerce; many of them began as market places, or places where merchants met to exchange goods.
Sometimes happening? Yes, of course. In many cases, one of a group of villages became the usual point where commercial exchanges took place, and over time the urban functions became more important that the agricultural functions; in some realms, for example in England, such a village may seek and obtain a royal charter declaring it a market town.
Some towns or cities were explicitly founded by organized settlement, at all times since the Antiquity, through the Middle Ages and up to very modern times; others grew from pre-existing villages; others grow out of support structures / camp followers for a military stronghold, or a temple, or an abbey. (Fun factoid: the -caster, -cester or -chester in Colchester, Gloucester, Lancaster, Manchester, Winchester is the Latin castrum, military fort.)
Not sure about the "huts" part; that depends very much of what counts as a hut and what counts as a house.
Examples of cities which grew out of pre-historic agricultural settlements include Rome and Athens, both of which show continuous inhabitation for thousands and thousands of years, On the other hand, Paris and London seem to have been set up for trade from the very beginning, starting most likely as meeting places for Celtic traders in pre-Roman times, conveniently located at cross-roads and fords.
In conclusion, all avenues are open. You can have a town set up by explicit settlement, possibly by royal charter; you can have a town growing organically around an abbey or a ford; you can have a town growing out of a place used for trade; you can have a town growing out of a village. Your pick.