First impression is the last impression is highly overrated and bias thinking. This mindset does not believe in any scope for improvements.
Life is all about continues improvements and NO ONE can be perfect at the first time. We have in life and in business many instances of great first impression and lousy impressions thereafter and vice versa.
Yes we have to give our best at the very first time but that is not all. We can always learn from mistakes, from others's experience , from customers feedback. First impression is not and can never be the last impression.
Yes , not improving continuesly is a cause for concern. Worrying too much about the first impression will pull you back to create any impression at all.
Try and create the great first impression and work to make it better at every next impressions.
First is not the last , first is just the first.