I am looking for a query to determine when the snapshot has been finished applying on the subscriber
I don't fully understand the part where you said:

but due to the internal rules and way of working I cannot change them

Could you elaborate on that a little more?...what can you not change, the actions of the Agent Job?
In any case, why not just start the existing SQL Agent jobs in a post-replication script using the system stored procedure sp_start_job?
You can specify the name or id of the Agent Job you want to run like this:
-- Executes the job by job id (unique identifier)
EXEC sp_start_job '53A3FA3E-2AAE-4FF1-A853-DEEC1FF494A2'

-- Executes the job by job name
EXEC sp_start_job 'AgentJobName'