Air carrier First Officer reported the flight crew had inadvertently crossed onto an inactive runway at ORD airport without clearance due to confusing signage at the intersection.

Narrative

We were ORD at Gate XX and it was my First Officer (FO) leg to fly; I briefed the taxi out and route for Runway 10L. We called Ramp for push; we then agreed on a single engine taxi based off seeing a long line for 10L. After contacting Metering we were told to hold short at the east side of the 'Y.' Ground then assigned us 9C via U; U7; Q; U2; cross 4L; G; hold short R.I read back the clearance and we both wrote it down; and agreed with the route. We began taxiing out; and the Captain advised me to remain heads up momentarily before changing the runway in the box.When we turned onto Q; I changed the runway to 9C and the Captain told me to run the runway change checklist; I then said we also need to start the left engine. The Captain said start the left engine and complete the delayed items; followed by the before takeoff to the line.While still on Q we briefed the runway change; and completed the engine start; we began the delayed items; but we were approaching Runway 4L at U2; I was looking right to clear us; I said 'clear right clear to cross;' then as we continued forward; the Captain asked if I see where G is; scanning back to the left; I saw a sign off to the left; and said 'I see G1' at that same time we crossed onto Runway 9R.We then expedited off the inactive Runway 9R at G1 onto G and held short R. ATC then told us possible pilot deviation and a number to call. We copied the number and then resumed the taxi and the flight proceeded uneventfully.Upon landing and going to the hotel; the Captain and I sat down together and called the number and called company. We explained what happened as outlined above; and ATC on the phone told us he understands what happened as that is a very confusing intersection and turn; and that the signage isn't very clear there.We were trying not to rush any checklists; but still were trying to get it done before crossing the runway; in the future we will be more slow and deliberate while crossing to ensure correct taxi route.