The Mexico international was signed from Guadalajara for a fee reported to be £2.2million earlier this summer.
But despite having spent almost seven weeks in Glasgow, the only public sighting of him in a Gers kit was a brief run out during their pre-season clash with Marseille.
The 27-year-old was an unused substitute as Caixinha’s team kicked off the Ladbrokes Premiership season with victory at Motherwell.
But the Light Blues boss hopes the extra workload he is putting Pena through will help him get up to speed quickly.
Speaking ahead of Wednesday’s Betfred Cup clash with Dunfermline, he said: “Carlos is having special training in order for him to get the right rhythm and levels.
“It’s specific work with him not just on the pitch but off it as well.
“That’s because when it’s the right moment we want to give him the chance.
“So far we think it’s not the right moment.
“We want to have him involved as soon as possible but he is getting there. He wants to be ready and we are working to make that happen.”
Gers’ 2-1 Fir Park win was a welcome relief for the Ibrox side following on from their Europa League embarrassment.
The Light Blues now kick off their League Cup campaign with a last-16 showdown against the Pars at Ibrox.
And midfielder Ryan Jack admits his side cannot afford to let the little roll of momentum they have built up with their encouraging end to pre-season come to a juddering halt against Allan Johnston’s team.
“Sunday was a good result and it gives us something to build on,” said the former Aberdeen skipper.
“After the friendly with Marseille a couple of weeks ago we sat down and spoke about how important it was for us to get the confidence and spirit back.
“We need to try and build some momentum. We’ve now carried that through the Watford and Sheffield Wednesday friendlies and then into Sunday’s match.
“It’s a good start and now it’s about pushing that on so that every game we go into, we do it with a spring in our step.”