GP and school tried to fob me off for a while when my DS was 6. I had to do masses of research and dig my heels in.
If you come prepared with a list of clear symptoms with the GP, you might be able to pass the barrier and get through to Paed.
My DS didn't really have obvious DCD traits. He crawled, walked early, he was very good at building Lego from young age.
The main sign was handwriting, and then coordination, catching balls.
His reading was late, so for quite a while I though he was dyslexic (which is not), DCD children often take more time than peers to acquire some skills.
He has attention issues, but they come from his DCD and his Auditory Processing Disorder.
You might to look into APD. Does your DS hear well when there is a background noise?
www.understood.org/en/learning-attention-issues/child-learning-disabilities/auditory-processing-disorder/understanding-auditory-processing-disorder#item3
APD comes with 5 Learning Difficulties: Dyslexia, Dyspraxia, ADHD, ASD, Language Disorder.
How was his phonics screening result?
Is he behind compared to his peers? Is he bright yet seems to struggle?
Because he's not 7 yet, school won't do anything, and even after because Ed Psych hours are very limited and offered to kids with severe learning issues.
But, you can start looking into the making sense of his weaknesses, and make a note of them.
There is a screening for dyslexia for children under 7 that can be done with a specialist Dyslexia tutor. If you search the Patoss tutor index, you might find someone in your region: www.patoss-dyslexia.org/Tutor-Index-Landing
When contacting a tutor, you might want to ask if they can do the screening, as I'm not sure if they all do it.