Salam Mia,
PLEASE overlook my previous answer! I made some changes but modification time limit was up so had to repost the whole thing! Really sorry for the inconvinience!
I hope this answers your question. When Adam's creation is discussed ,Allah says He breathed something into 'bashar' and it became 'insan' another creation unique in every sense, Adam did not have a set of parents, but he was created by Allah the creator. He can create what He wills without a set of parents in case of Adam, with use of one parent in case of Jesus, and both parents in case of me and countless others. That is the nature of creation, creation requires two parents in most cases. But it is a law of nature He created and He only bends it when He is showing us His might and majesty as creator. He can create without parents, He is not bound by laws of nature He created. But He also informs in verses discussing Jesus and Adam that divine intervention took place beyond normal human creation process in their respective creation, i.e Allah intervened in a way that is not done normaly. But that does not mean in the creation of others He does not play a role, everyone of us are unique genetically and possess an independent soul. Each creation is a wonder proclaiming and representing His might and majesty to the world. Also Adam did not create himself, he had a creator and Jesus was not created by Mary, Allah created them albeit in a different way! At one point something existed which did not have a creator and is alone, that is Allah! Allah never said He created Himself, then He would have had a beginning and a creator, Himself! But He said He was not begotten, He existed always. Also if creation is discussed on a cellular level, it happens in two ways, mitosis and meiosis, meiosis requires two gametes from a genetically compatible pair! This is ruled out as Allah is one of a kind! So we are left with mitosis, this does not happen simply because He says He does not begot and also it may very well be that both mitosis and meiosis are attributes of the created not the creator! Astagfirullah!
When He says how can He create when He does not have a consort, He is making a reference to our understanding of the natural law of life creation, two parents required to create a new creation. He is not making a statement about His ability to procreate or requirement of a consort to do so.
Also, if we look at our children and spouses and that of other species' they are not created by us, even among the created, procreation and marriage does not take place between a creator and his/her creation. This never happened and is not a phenomenon that occurs in nature. Also you said yourself true progeny is gentically related in sight of Allah, so this genetic procreation is ofcourse not possible as Allah does not have a consort that is non-created like Him or shares his nature! Also if He creates a son or daughter without consort, they will still be created by Him! And declaring something He created as His consort or his progeny is unfathomable. Plus He says so in the Quran calling someone your son does not make him your son, it is not the truth. The only possibility of Allah having a son or a consort is if He creates one and gives them these designations. But they will be creations nonetheless as He is one of a kind and not another entity sharing his nature ever existed or will exist!
One must understand one thing the creator is different than the created. The creator is an entity about which we have no knowledge other than what He revealed and He revealed Himself as the entity that existed always, He is one, He was not begotten and nor does He begots, in other words He does not have parents and nor any progeny. He does not have a beginning or a continuation in the sense of having descendants. He describes Himself as above all this! He is one so if He takes a consort( astagfirullah) it will be created by Him. And How can the creator and creation be equal! A marriage is between people belonging to the same species and He is alone! Even as humans most of us do not want to consort with living things that do not belong to our species and also with something that we created. We regard such things as shameful. How can God have a consort then, when He has no equals and we as the created find consorting with living beings below our station specieswise or otherwise distasteful! He has declared himself beyond the need to have progeny, or any kind of spousal or familial companionship. All these attributes of having parents, spouses, children are attributes of the created. And created by a creator for a purpose. We have needs as the created, He is beyond any kind of needs. He chose to differentiate Himself from His creation as an entity that does not procreate. It is simply an attribute which makes him unlike any creation we know! Besides Allah says in the Quran if there were multiple Gods there would have been chaos, He asks us to reflect and ponder about the harmony that exists among the creation because of Him being the one and only and having no needs physical, emotional, spiritual or otherwise. The Supreme and Everlasting!