Oracle query is slower the second time
Cases like this can usually be solved for certain by enabling trace events 10046 (if you have authority to do so), and run tkprof on the resulting trace files:

alter session set events '10046 trace name context forever, level 8';
select /* try one */ -- add your SQL here and invoke it;
select /* try two */ -- add your same SQL here and invoke it;
show parameter user_dump_destination


Invoke it a few times, and then turn tracing off, log off to ensure the trace files get closed:

alter session set events '10046 trace name context off';
exit;


Then find your trace file, and run tkprof on it, assuming your trace file name is ${ORACLE_SID}_ora_39110.trc:

cd $ORACLE_BASE/diag/rdbms/$ORACLE_SID/$ORACLE_SID/trace
tkprof ${ORACLE_SID}_ora_39110.trc ${ORACLE_SID}_ora_39110.trc.txt
vi ${ORACLE_SID}_ora_39110.trc.txt


The output of tkprof will show you execution statistics (logical reads, physical reads, etc). And you can look at the actual trace file if the tkprof output doesn't help.

If that doesn't help, you can enable 10053 event, and enjoy wading through thousands of lines of output; but sometimes you need to do that.

But first things (well easier things) first; do as others suggested; see if table statistics are up to date, optimizer settings, etc.  If you are using the exact same criteria each execution, could be the optimizer is "on the border" on plans.  I would ensure you have collected system statistics; see the documentation on dbms_stats.gather_system_stats pl/sql package.