Here is how to actually influence a meeting you will never attend.
First, document impact as it happens, not in the week before review season. Write it in outcomes a stranger could repeat, not activity only you would recognize as hard.
Second, make sure your manager has what they need to advocate for you specifically, not just generally. A manager walking into calibration with one strong example wins more than a manager walking in with a vague sense that you are solid.
Third, build visibility above your manager before calibration happens. A skip level who has seen your work firsthand is worth more in that room than ten more hours of effort your manager alone can see.
None of this is about gaming the system. It is about making sure the system has accurate information about you when the decision actually gets made.