Is there a way to use Fmrte to speed CA up? I heard for example that maxing out the ambition and professional attributes leads to a quick CA increase but I tested it out and it makes little difference.

Ambition, determination and professional attributes as well as increasing a clubs training facilities. They need to be playing fairly regular first team football if they are over 20. If they play well I also think that contributes and if you send them out on loan I think attributes rise faster if they are loaned out to a playable league.