This doesn't need to be complicated.
The standard requires that your people be competent (skilled).
It requires that you determine what those competencies (skills) are for each position.
It requires that you determine that they have those skills, and if not, what you are doing or have done for them to obtain those skills. That is usually training.
It requires that you determine that what you did is effective.
It requires that you keeps records about how those skills were obtained.
The needed skills are frequently included in job descriptions, but they also could just be a list or even part of a matrix. This should not be hard to develop. These can be described in broad terms so that any one position could be covered in roughly 1/2 dozen to a dozen categories or perhaps a few more. You certainly don't need a hundred of them.
To avoid going backward and trying to create training records for your existing employees, you can grandfather them, indicating that they have already proven their ability to perform as expected. Grandfather statements often also include that they have been trained to the ISO/AS requirements that are pertinent to their position. Even if grandfathered, you still need to have a list of needed skills though.
Skills that an employee brings with them from education or prior experience can be shown with job applications, resumes, diplomas, certificates, etc.
Verification of the effectiveness of training (or other action taken to obtain the needed skill) can be in any of several ways. A common thing is to have a manager go out and observe the work of the employee a month or two after training and confirm that it was effective. Keep a record of this.
Another can be to have employee evaluations (if done, this is usually an annual thing).
Another is to monitor the process that he is functioning in. So if he is in production and you production KPI is First Pass Yield of Final Inspection (how may things make it through final inspection without rework), then showing that the KPI did not drop off due to the new employee. Other performance data may also be important, such as on-time delivery and customer satisfaction.
So determine what you actually do now, determine how you can effectively answer this with the least reconfiguration of your company, and get it done.
As Randy would say, it's not rocket science. Or as Marc would say, it's just basic stuff.
