I have one question for everyone. How do you resolve your issues if you have issues with your manager or lead? Or How do you build a trust if the trust is broken because of some delayed work, wrong work, wrong design, or something you did wrong in the past and he/she still judges you based on that but you're now doing better?
Apologize, accept the mistake (if genuinely on your part), and move on in career. Don't overthink it. You won't be working there forever.
First impressions is last
Mistake can happen we are human just avoid big mistake.
If you think trust is broken just switch the org no other option
Resign
The only way to regain trust is to build processes. Tell the other person, I screwed up last time. Here is the new process I am trying to build so that this does not happen again. Tell them no one joins a company or a team with bad intent. become a part of the solution (even if u were the problem last time). every manager will appreciate it.