A 3 kW generator does not have enough power. Generally, the generator power coefficient is 0.8 (not necessarily). It is written on the generator nameplate. If it is 0.8, the actual power generated by the 3 kW generator is 2.4 kW or less.
The starting current of electrical equipment is approximately three times higher than the rated current. If 2.4 is divided by 3, your generator can generate 800 W and less. If it exceeds the limit, it will be difficult to start. If the starting current is too high, the generator will be overloaded and an inferior generator may even burn out.