After swithover, Primary db open before standby db comes back (mount)?

we did a dataguard switchover using dataguard broker.

I watched the logs , it did this in below sequence

1: Pre-primary switchover to physical standby successfuly

2: Pre-standby switchover to primay successfuly

3: current standby(pre-primary) reboot to mount

4: current primary (pre-standby) open

From the log , step 3 is a pre-requisite of step 4. without current standby  come back (mount), current primary will not open in our switchover, step 3 took 10 minutes, so it caused 10 minutes outage.

My questions is: is it possible, (step 4) "current primary" open without step 3? because switchover has been done successfully, primary database can open first, even though standby database is still not up. if this is achievable, then we can avoid our "10 minutes outage". primary comes back as soon as possible(first) and standby database comes backup later.