Hi OP,
As a mother of 4 who have different (likely) genetic/congenital diagnoses, if I may offer my twopence worth:
My eldest child's diagnosis at 17 came as a total bolt out of the blue when he needed a very specific kind of medical for future career. We already had 2 younger children suspected of a syndrome genetic in origin and my second eldest child had been diagnosed with autism with a familial link.
We have been on a genetics journey since DD (youngest) was born 15 years ago. In her first weeks of life it became apparent that that she had significant health and physical needs which have only become more difficult to manage year on year.
She has had extensive genetic testing, based initially on very specific diagnoses that can present with several different gene mutations. All came back negative. She then needed a skin and muscle biopsy which led to further head scratching. By the age of 4, we had been enrolled on the DDD study and then a few years thereafter on the 100,000 genome study
So far, despite such extensive testing nothing has been found to explain her multitude of disabilities; at times this has been very isolating and upsetting, not to mention very hard to explain to well-meaning friends and family who think it's good news every time a test comes back negative (& there have been some really terrifying potential diagnoses throughout this time so yes some of those not found have been a cause of relief) but the not knowing is a very difficult place to dwell in too.
With kindness, if it has been suggested by Doctors that it's likely your son has a genetic condition, this assumption will not have been made lightly and only with a view to the best interests of your child, yourselves as parents, plus potentially for any of your future children. My eldest DS is now keen for answers to as he and his fiancee are thinking about children of their own.
Historically it has been very difficult to get testing for many families and now we are learning and understanding so much more about genetics and the role they play, not just in the short term but also in longer term health care planning, knowledge is very much power. If a diagnosis does come back, it may even be possible to prevent certain conditions from developing further down the line using medications or even gene therapy. At the very least, it will ensure support is put in place at the earliest opportunity and any scans/tests/monitoring can be appropriately scheduled.
You may get a nothing found result or a variant of unknown significance (broadly they can't be sure what, if any relevance, it may have at the point of identifying based on knowledge to date) and that can bring a whole other host of emotions too.
Having walked in very similar shoes to you, I found those very early years in DD's life extremely difficult and it plagued my every waking (and sleeping) moment. Now that you have been told there is even the possibility of a genetic condition, I think even if you decide not to proceed or to pause testing for now, you may find you can't stop your mind from going to scary places.
If you can, please try and seek support - your GP, health visitor and genetic counselling services should be able to guide you and if you aren't already aware of SWAN UK - Syndromes without a Name please do have a look
I have name changed for this post as my reply is quite identifying to those who know me but I wish you well (sorry this is so long)