I'm wonder how much read model delayed? What reason(s) cause it for delay? If I have only little preprocessing process data for read model. I have no experience at scale.
"It depends." The cause of the delay is the propagation of the information from the data structure that supports the write to the data structure that provides the read. So some of the difference is in the distance between the two data structures, some in how much work is required to fold the new information into the read model, and how much time there is between the write, and the start of the process to copy that information to the new data structure.
Another way of thinking about this is that the "clock" of the read model runs slow compared to the write model; so the read model is describing what things look like "now", where now is some time in the past.
So one thing that you can do in some cases is to make that clock explicit; "show me what the model looked like at time = t"; or "show me a recent model after time = t" is a query that the client can send to a read through cache; where the query handler can simply look to see if its copy is recent enough to satisfy the query, and if not pull a more recent copy of the data.
We say "read model" and "write model", but fundamentally there's nothing wrong with reading data from the write model -- identify the most recent write model available at the time of the query, and then (synchronously) build a representation of the query response, to return. That gets you a more "recent" version of the read model, at the cost of some extra time processing the query.
Also, you don't have to use the same caching strategy for all queries; for instance, you might use a cached read model when showing a user somebody else's character, but using a fresh read model when showing a user their own character.
Part of the point of CQRS is that you can make these decisions on a case by case basis.