Got it; if you set the log level for the job to DBMS_SCHEDULER.LOGGING_RUNS, the database will record the enabling time:
alter system set job_queue_processes = 1;
BEGIN
    DBMS_SCHEDULER.CREATE_JOB (
            job_name => 'INFINIT_JOB',
            job_type => 'PLSQL_BLOCK',
            job_action => 'begin loop null; end loop; end;',
            start_date => null,
            end_date => null,
            enabled => false,
            auto_drop => false
    );
 
    DBMS_SCHEDULER.SET_ATTRIBUTE( 
         name => 'INFINIT_JOB', 
         attribute => 'logging_level', value => DBMS_SCHEDULER.LOGGING_RUNS
    );
    dbms_scheduler.enable  ( 'INFINIT_JOB' );
    
END;
/
select job_name 
from   user_scheduler_running_jobs;
JOB_NAME      
INFINIT_JOB  
BEGIN
    DBMS_SCHEDULER.CREATE_JOB (
            job_name => 'TEST_JOB',
            job_type => 'PLSQL_BLOCK',
            job_action => 'begin null; end;',
            start_date => null,
            end_date => null,
            enabled => false,
            auto_drop => false
    );
 
    DBMS_SCHEDULER.SET_ATTRIBUTE( 
         name => 'TEST_JOB', 
         attribute => 'logging_level', value => DBMS_SCHEDULER.LOGGING_FULL
    );
    
END;
/
select job_name, state, next_run_date
from   user_scheduler_jobs;
JOB_NAME      STATE       NEXT_RUN_DATE   
INFINIT_JOB   RUNNING     <null>           
TEST_JOB      SCHEDULED   <null>    
exec dbms_scheduler.enable  ( 'TEST_JOB' );
select job_name, operation, log_date 
from   user_scheduler_job_log
where  job_name = 'TEST_JOB'
and    log_date > trunc ( sysdate );
JOB_NAME   OPERATION   LOG_DATE                   
TEST_JOB   ENABLE      01-FEB-2021 09.20.01 +00