B737 FLT CREW INADVERTENTLY DEVIATES FROM ASSIGNED DEP CLRNC.

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CAPT'S LEG; BRIEFED LNAV AND AUTOPLT ENGAGEMENT ALTS AT GATE FOR AACES 1 RNAV DEPT LAS. COMPLETED ALL IRS ALIGNMENTS/UPDATES. UPON TAKING THE RWY; CAPT ADVISED ME HE HEARD LAS OPS TRYING TO RAISE US ON COMPANY FREQ. WE IGNORED THE CALL AS WE WERE ABOUT TO RECEIVE OUR TKOF CLRNC ON RWY 19L. AFTER TKOF; CAPT ENGAGED LNAV AT 400 FT AND THEN CALLED FOR 'FLAPS 1 DEG; CLB THRUST AT 1000 FT.' I DID NOT CONFIRM WHETHER HE ENGAGED THE AUTOPLT AT THAT POINT. HE REQUESTED THAT I CHK ON WHAT COMPANY WANTED AFTER WE FINISHED CLEANING UP THE ACFT; AND ALTHOUGH WE WERE BELOW 10000 FT STILL; IT DIDN'T SEEM LIKE AN UNREASONABLE TIME DUE TO SECURITY CONCERNS -- WE HAD EXPERIENCED A DELAY IN BOARDING WITH PAX NOT FOUND; THEN FOUND; BAGS ON/OFF/ON AGAIN; ETC. I LEFT FREQ; AND COMPANY ADVISED THEY HAD NO MESSAGE; APPARENTLY THEY WERE JUST UNAWARE WE WERE DELAYED OFF THE GATE AND THOUGHT WE HAD FORGOT TO CALL TIMES IN. UPON RETURNING TO LAS DEP FREQ; THE CTLR ADVISED US THAT WE HADN'T YET BEEN GIVEN A SHORTCUT ON THE DEP; TO TURN IMMEDIATELY TO HDG 180 DEGS. I LOOKED DOWN AND SAW US OFF THE DEP; AND INQUIRED OF THE CAPT WHETHER WE HAD RECEIVED A VECTOR WHILE I WAS OFF FREQ. AFTER SOME INITIAL CONFUSION; HE REALIZED THAT THE AUTOPLT HAD NOT ENGAGED; ALTHOUGH HE HAD THOUGHT THAT HE SELECTED IT. THE CAPT'S FAILURE TO CONFIRM THE AUTOPLT ENGAGEMENT; MY FAILURE TO BACK HIM UP WITH THE ENGAGEMENT; A LACK OF POSITIONAL AWARENESS DESPITE THAT MAP DISPLAY RIGHT IN FRONT OF BOTH OF US; DISTR FROM THE OPS CALL; AND THAT GOOD OLD 'RUSHED OUT OF THE GATE; WE'RE LATE' FEELING CONTRIBUTED TO THIS EVENT. A POSSIBLE SOLUTION MIGHT BE TO INCLUDE SOME TYPE OF CALLOUT ABOUT THE AUTOPLT IN SOP'S FOR RNAV DEPS. AT 1000 FT; WHEN THE AUTOPLT SHOULD BE COMING ON; THE PNF IS DISTR WITH FLAPS AND SETTING CLB PWR AND ISN'T DELIBERATELY PLACED IN THE LOOP ABOUT THE AUTOPLT ENGAGEMENT.