When I watch us I just don't see a team that is looking to play possession based football, that is my gripe. To me we look more like a team that is built to try to play in fast transitions. Do we want to press? ETH says we do but I'd say our press has been average to non-existent so far. We build a lot in wide areas and in some games have focused heavily on putting crosses into the box. This is where I am at odds with when some claim he is a possession based manager. I imagine in Eredivisie that Ajax dominated possession by default as they had much more quality compared to the other teams - they were the Man City of that division such was the gulf in quality. Particularly going back to around 2019 when they had a good group of players come through their system.
Watching the highlights and reading the stats from the Real Madrid game that you reference, I feel this only backs up my point. They scored 3 goals through turnovers and quick transitions, with the final goal coming through an outrageous freekick. The stats suggest Real Madrid dominated the game in terms of possession, despite the scoreline. Sounds familiar (Arsenal, Leicester and Liverpool this season).
Fair enough, it will absolutely take time to implement his style. However, I don't see the 'makings' of a possession based side or a team that is building towards that right now. In my opinion you have to be dominant to be a top team, so that is the natural progression that I am looking for. I'm not calling for his head, but more looking for reassurance that this is what he is trying to do. Pep and Klopp struggled initially but I watched City and Liverpool and could see what they were trying to do. I've seen many managers take over worse teams and stamp their style on a team quickly - even if results were further down the road whilst it was perfected.