The journey to Murrayfield starts at Raeburn Place tomorrow with a home clash against Division Two rivals, Jed-Forest.
However, all Premiership-class teams are initially drawn in qualifying groups of four and Cross says: "I strongly suspect that the chances of underdogs having their day in the type of poor conditions which can act as a leveller have been reduced by the group format.
"It's always possible, though, that we can perform creditably in the Cup again given our core of experience provided by the likes of Iain Berthinussen, Dan Teague, Greg Campbell and Nathan Pike.
"They are all helping bring through players such as Sam Atkin, our young threequarter, who is definitely one to watch for.
"The great thing for both myself and fellow coach Jonny Els is that our experienced guys are absolutely driven in their quest to get Accies back to the First Division where they feel the club belongs.
"That makes me feel a bit easier going into a match like tomorrow's against Jed because nobody will be allow to let up and damage the momentum we've been generating."
The message from Cross is that the start of the Cup competition, which also has them pooled with Glasgow Hawks and Dumfries, may be a prelude to the start of the new league structure which will see Accies in group two and aiming to win all seven fixtures standing between them and a return to Premiership Division One in 2011-12, but there remains plenty of incentive.
In looking to kick-start their cup bid Accies can draw on the fact they have already beaten Jed in the league, albeit by 22-20.
"To be fair we were leading 22-6 going into the last ten minutes when we leaked a couple of tries.
"Fortunately our defence held firm when Jed attacked us in the final play and we'll look to repeat that victory with a side that has Sam Atkin operating on the wing as opposed to centre where he has started in each of the past three games.
"As a member of the extended Scotland under-20 squad it is important that Sam has a full skill set. Playing him at centre has added to his passing ability."In one other respect Cross, the former Edinburgh captain, is highly satisfied.
"Last week we comfortably defeated Stewart's Melville and the line-ups were similar to when they effectively relegated Accies with victory on our pitch last year so that was a good sign."
Watsonians add Ben Di Rollo, Niall Dennis, Chris Scott and Ed Hunter to the squad which lost to Dundee last week when they entertain Kirkcaldy.
Boroughmuir welcome back age-group caps Stevie Wilson and Tom Bury to their threequarter line at home to Dalziel.
For Stewart's Melville there is an early opportunity at Inverleith to atone for a recent league defeat by Hillhead/Jordanhill bit injury woes have continued however as Stuart Ker suffered a broken hand and full back Liam Steele collected a knee injury last week at Accies.
Currie head for Hamilton with James Johnstone replacing Edinburgh pro Andy Turnbull on the wing. Noting how Hamilton lie second in Division Three, coach Ally Donaldson says: "We'll give them respect."
Heriot's are at Cartha QP without Cammy Ferguson and Max Nimmo but player of the month winner Glenn Bryce is listed.