THIS ARTICLE WILL CONTAIN SPOILERS FROM THE LATEST EPISODE OF ARROW "SEEING RED" SO READ AT YOUR OWN RISK.
In the latest episode of Arrow, we learn that Oliver got, a yet to be named, young lady pregnant seven years prior to the show's current timeline. We know that Oliver doesn't know that the unamed female was payed off by Moria Queen to lie to Oliver about having miscarriage. Given that the show teased that Oliver is actually a father to a, yet to be revealed child, it's safe to say that the child do exist in the Arrowverse, even though it's yet to be 100% confirmed.
In the comics Oliver has three sons, Roy Harper(adopted), Robert Queen(son of Shado), and Connor Hawke(son of Sandra Hawke). Roy already exist in this universe, and I highly doubt they'll mess with the source material and have a twist where Roy is actually Oliver's son; it was teased that his unamed child would grow up in Central City and we know Roy grew up in Starling City. Given that Shado is dead(?) and that the young lady Oliver impregnated was indeed not Shado, the child is unlikely to be Arrowverse's Robert Queen; the child most likely will not know of his father, so he would take his mother's maiden name, and with the unamed mother being payed to keep distance from Oliver, naming the child after his grandfather would not be wise. Even though there is probably not an Arrow fan out there(that knows their Green Arrow source material) that doesn't believe the unamed child is Connor Hawke and the mother is Sandra Hawke, these are the reasons why I believe, if the child is male, that it is indeed an Arrowverse Connor Hawke.
This theory will indeed be a long shot, but here me out. While I am extremely happy that Connor Hawke may possibly exist in Arrowverse, I was a little bit disappointed when I realize he'd be no more than 7 years of age in the current timeline of the show. This disappointment led me to the theory that A.R.G.U.S, maybe with Cadmus Labs as a subdivison(if they introduce Cadmus on the show) accelerated Connor Hawke's aging process. Why? How? In a previous episode of Arrow, we learned that Oliver and Amanda Waller have some form of past together, most likely during the time Oliver was missing for five years. If Amanda Waller was associated with Oliver, during his time on the island, she probably knows what he went through, to be forged into the weapon he is now. It's known that Amanda Waller has gripes against heroes and vigilantes, unless they can be controlled by her. With her knowledge of what Oliver has gone through on the island, and a huge government agency in her pocket, she could easily learn that Connor Hawke is Oliver's son, remove him from his mother, have a lab(Cadmus?) accelerate his aging process, plant fake memories, then stage a similar experience that Oliver went through on the island, for Connor to endure, fake a rescue, and then she'll have her own personal Arrow to control. Why would she need Connor? Well, similar to how Terry McGinnis(Batman Beyond) was created. In the DCAU Amanda Waller went out of her way to create a Batman for the future by altering Terry's legal father's reproductive system, making his sperm consist of Bruce Wayne's DNA. Amanda knew it would take more than just putting someone through a similar experience as another, to get similar results, so she got rid of some of the variables by making her futre Batman, Bruce Wayne's son. In this case, Oliver already has a son, so she doesn't need to go to as great of lengths, to forge a new Arrow.
So what do you think? Do you think the theory is possible? Let me know below!