This is a very difficult question to answer, and it's probably the reason that persistent, player power modifying changes are not included in most card games.
one possible solution is a central online data store/mobile app
This may be beyond your project, but one solution would be to implement some form of website wherein player profiles can be stored, this website would allow you to keep control of player profiles, and give players confidence that their opponent cannot (at least, legally or easily) compromise the data stored in your database.
Depending on how your system works, registering win/loss may be enough for tracking advancement, in which case players can each register a match and its result (or one player can propose a match/result, which the other must confirm).
If characteristics of the match must be tracked as well (e.g. if casting a certain type of spell increases a certain statistic) this can also be tracked in a similar way, just requiring some more detail on behalf of your players.
All of the above however only solves the problem of individuals trying to cheat. If a pair or group wish to cheat, they could just register alternating wins/losses against each other to advance at a high rate. Diminishing returns could be included to combat this, however it would still not resolve the issue of a larger group gaming their stats in the run up to a large tournament (you can only limit this behaviour so much before you have a negative impact on small play groups who regularly play against each other)
Another option would be to produce something similar to how planeswalker points are handled in Magic: The Gathering, which is that your tournament record is uploaded by the tournament organiser (using software provided by Wizards of the coast, who make MTG, which uploads the list of all players, all matches that took place, and who wins each match). This removes the opportunity for any size group of players to cheat, providing that your tournament organisers can be kept trustworthy (keeping your tournament organisers invested in being trustworthy by giving them a lot of rewards like free promos/product, and then removing all rewards and all ability to organise play where that trust is broken). This would allow you to track player movements in probably the most secure way possible, and does not require the same production of a full featured mobile app that players can (and crucially, enjoy) use to track their play.
I will say one thing however. There is a reason no other card game has an advancement system, and it isn't that no one has thought of it before. It is difficult enough to keep play fair without a system like this which can be potentially gamed for an advantage. Card games (particularly collectible ones) have a big enough barrier to entry already, in that cards can be particularly expensive, having an innate disadvantage from being new BESIDES not owning all the cards is going to have a significant impact on getting new players into your game. Getting new players and keeping them has to be absolutely one of your top priorities, because players leave all the time, and if you don't have a steady stream of new players coming in, you will kill your game stone dead. Nobody plays a game if they cant play it with anyone, and if no one new takes it up, it will fizzle out very quickly.
A better solution is to reward regular players with Aesthetic bonuses, such as Promos, Shiny things, free stuff that no one else gets. This encourages long term play as well (if not better) as tangible game advantage, without discouraging new players (in fact, it encourages them to stick with it)
