The image of therapy as an hour spent talking about your mother comes from psychoanalysis and describes a small part of what is practised today.
Cognitive behavioural therapy works mainly with what is happening now: what you think, what you do, what maintains the problem. The past appears only as an explanation for where a belief came from, not as the main terrain.
Psychodynamic therapy goes there more often, because its premise is that current patterns are understood through those formed early.
Schema therapy sits in between: it identifies patterns formed in childhood but works them in the present.
Trauma-focused therapies go into the past by definition, but with specific stabilisation procedures first — you do not start with the hardest event.
What holds across all of them: you are not obliged to say anything you are not ready for. “I don't want to talk about that now” is a complete answer, and a therapist who insists is making a mistake. In trauma work, pace is part of the treatment rather than an obstacle to it — going too fast can retraumatise, and that is known and deliberately avoided.
Worth knowing nonetheless: if questions about childhood produce a strong reaction — irritation, blankness, a sudden urge to change the subject — the reaction itself is information, whether or not you go further. It is something to mention, not necessarily to explore immediately.
If you have a clear preference, say so in the first session. It is information that helps choose the method, not an awkward demand.