Can you activate a planeswalker's minus ability the turn you cast it if it has enough loyalty?

Planeswalkers do not have summoning sickness in the way creatures do. The restriction on activating loyalty abilities (CR 606.3) simply states that a loyalty ability may only be activated once per turn, and only during your main phase when the stack is empty — there is no rule preventing activation on the same turn the planeswalker entered the battlefield.

When you cast a planeswalker, it enters the battlefield with a number of loyalty counters equal to its printed loyalty value (CR 306.5b). To activate a minus ability, the planeswalker must have at least as many loyalty counters as the ability's cost (CR 606.3). If it does, you may activate that ability immediately.

The once-per-turn limit (CR 606.3) means you can only activate one loyalty ability on a given planeswalker per turn, regardless of whether it is a plus, minus, or zero ability. So if you activate the minus ability, you cannot then also activate another ability on the same planeswalker that turn.

Example: You cast Chandra, Torch of Defiance, which enters with 4 loyalty counters. Her −3 ability requires removing 3 counters. Since 4 ≥ 3, you may activate it immediately during the same main phase, leaving her with 1 loyalty counter — no waiting required.