Gravity acts as the container. It takes cold gas, otherwise the kinetics involved keep the gas dispersed like you state. But once the gas cools enough it no longer has enough energy to hold itself apart against gravity and begins to contract. This of course starts increasing the temperature of the gas, but momentum inwards and the increasing gravity from the larger mass contracted into a smaller volume fight the outward push from the increasing heat. Eventually the heat being generated will blast away the further parts of the in falling gas that were too far away before the new star got too hot.
Edit for grammar. Typing is hard.
Gravity.
Even in a closed container on earth the pressure is higher at the bottom than the top because of gravity.
Do that with a big ball of gas in space and it’s enough to pull the gas tight enough to start fusion. Just like on earth, the pressure is higher as you go to the center. The star is just FAR larger.
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