Having bigger muscles does not make you stronger
Contrary to what many gym bros might want you to think, bigger muscles do not always equal more strength. Of course, larger biceps have an advantage, but the key to getting strong lies in the intensity of the workout, not in its bulking ability.
In this photo, the woman has smaller muscles, but she can still lift the weight of the massive guy sitting on her shoulders. This is proof that bulking up is not necessary if you wish to grow stronger.