What you would typically do in a case like this (if I understand it
correctly) is that in the s_input ioctl you first select the input in the
subdev, and then you can call the subdev to determine the standard and
format and use that information to set up the bridge. This requires that
the subdev is able to return a proper standard/format after an input
change.

By also selecting an initial input at driver load you will ensure that
you always have a default std/fmt available from the very beginning.

The default input is 0. So you mean I ask the subdev std and fmt in
probe instead of open?

It also looks like the s_input in the bridge driver allows for inputs that
return a subdev format that can't be supported by the bridge. Is that correct?
If so, then the board code should disallow such inputs. Frankly, that's a
WARN_ON since that is something that is never supposed to happen.