A muscle will improve regarding strength, much earlier than 2-3 months. Initial gains in strength will be due to improved neural recruitment and exercise technique. It will also depend on applying some principles of exercise. These are frequency, duration and intensity and the overload principle. I would expect strength gains in 1-2 weeks. Obviously there would not be the same changes in muscle architecture that is seen at a 3 month period, which is generally accepted as being the period of time needed for muscle hypertrophy.
Motivation and discipline are also important to any exercise regime.