How to Trigger Another Jenkins Job with Downstream Jobs and Resume Only After Success?

I have a Jenkins setup with two main jobs: TEST and INTG. The INTG job has several downstream jobs that need to run sequentially and some parallely. My goal is to ensure that when I manually trigger the TEST job, it first triggers the INTG job and all its downstream jobs. The TEST job should only resume after all INTG and its downstream jobs have completed successfully. This setup is crucial because I want to ensure that any issues in the integration environment are resolved before the code progresses to the test environment.

I need it to set this up a maven project and not as a pipeline project.

I have tried using a connector job which is linked with the TEST and INTG Jobs and upon the successful completion of all the INTG Job only the connector job should give success status and based on the status of the connector job, the TEST job will resume or fail the build.

While this works in the case if i have downstream job in INTG executing sequentially but this fails to parallely trigger two jobs and wait for its result.

Is there any other approach available to meet the following requirement?