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"P" is Program mode. The flash won't pop up in this mode unless you tell it to with the manual flash button.
You might be better off starting in Av (Aperture Priority) mode and choosing the depth of field you want via the aperture setting.
The camera will then pick the shutter timing according to the available light.

Choose a smaller number (=larger aperture) for less depth-of field, meaning the background will appear more blurred.

Choose a larger number (=smaller aperture) for more depth-of-field meaning the background will be more in focus.