Air carrier Captain reported difficulty finding the proper taxi line after a deep ramp push by the tow crew. There was no taxiway line the pilots could see. The Captain also stated the ramp lighting in ONT needs improvement.

Narrative

During our push back at ONT from gate at XA:17am. We were pushed very deep on the ramp at a slight angle facing our direction of proposed travel for Runway 08L. This was prior to sunrise (XB:54am local time) and the ramp area was extremely dark. During the push back we were cleared to start engines. During the start of Eng 2...we [were] distracted by an ECAM message. ENG 2 OIL TEMP LOW. The new hire first officer was startled with this ECAM. I was explaining to him this was normal during cold weather starts; was when the aircraft reached it stopping location of the push back. After the push back crew left to return to the terminal; we started to taxi making a left turn. We were verifying the #2 Engine was now at normal temperature. Its then I noticed the lack of a taxi surface markings anywhere in front of the aircraft. I quickly check our position on the (Airport Information) page; only to find accuracy was off and our position was showing somewhere between Taxiway NI and N (which would have been on the other side of the blue lights).I started a small left turn then corrected with a hard left turn. At this time I noticed that the ramp/taxiway edge surface marking was to the right of the aircraft. I continued over to and joined Taxiway N1. There is a very wide hard surface area between the edge line and the blue taxi lights. With the deep push from the ground crew; we had inevitably started to taxi between the edge line and the blue taxi lights in the dark. We joined Taxiway N1 at this time. Distraction with engine start ECAM and loss of exact aircraft position with deep push back. Only using taxi light on extremely dark ramp (should have used more of the lights than I had available (Turnoff/landing). Better lighting on the ONT ramp; aircraft not being pushed so far off the taxi line; and using all available aircraft lighting. I know at other US airports; non-movement areas are marked with diagonal yellow striped lines.