Can I have 2-layer design with PCIe connector?
PCIe needs to be referenced to ground to get a single-ended impedance of 60 ohms, in addition to the 100 ohm differential impedance. This would be very hard - if not impossible - to achieve using 2 layer rules and reasonable trace sizes with the .063” thickness PCIe boards have to have.

Further, if there are islands of ground between pairs in an attempt to provide an edge-coupled reference, these islands will be shared with adjacent pairs, leading to crosstalk issues.

If you were only doing 1 lane - might be possible. More lanes?  Don’t think so.