How is HCM confirmed?

https://www.mayoclinic.org/diseases-conditions/hypertrophic-cardiomyopathy/symptoms-causes/syc-20350198
Welcome back @lpaelevated4 , I posted a link to the Mayo Clinic on HCM.
I hope you find it informative as you try to put together your heart story.
I am not a cardiologist, and I don't play one on TV! Cardiologists come in all shapes and sizes, just like we do, and a lot of folks with HCM go misdiagnosed for years before they finally get a real straight answer to their symptoms.
I was a big time walker/runner/hiker/biker/ballroom/swing dancer. I was in great shape. And then I noticed I was struggling on some hikes in higher elevations. And couldn't make it through a cha-cha-cha without being winded. I KNEW something was wrong, but my local cardiologist was unable to come up with anything. He said I had small vessel disease and to drink more water. Then I had a really bad murmur, then I had aortic stenosis, then I had a super rare congenital heart disease called Sub-aortic Membrane that needed surgery right away! And he would refer me to our local heart surgeon.
I was stunned.
First, if it was SO RARE, how many had this local heart surgeon done?
That's when I went outside my area and was seen by two COEs (Center of Excellence) and another affiliated with the hospital I worked for.
I say all this to show you that it make take time and effort (on your part) to reach the correct conclusion and what you really have.
HCM is a master of disguise and can lead a cardiologist down the wrong road. That's why it is super important to do your own research once you find out what you have.

Take some time and read up on HCM, but again...since you don't know what your diagnosis truly is, you don't want to get too far out in front of this process. Does that make sense?

In addition to those tests I also had a dobutamine echocardiogram and a cardiac MRI with contrast. Those two tests provide better detail info to make decisions.

I would like to add to Debra's very informative comment that finding a cardiologist well versed in HCM will be worth your while. I am truly amazed at how many different heart diagnoses are possible and cardiologists each often pick a few of them to study and specialize in. If a COE for hearts is not far, as she wrote, it will be worth affiliating with them. There are well-versed HCM cardiologists in other places such as the one I have seen for many years; there is no COE here. He was quick to refer me to Mayo when I arrived at that point in my journey. You will learn much about HCM as you go along and become a partner with your cardiologist in navigating your journey. Knowledge helped us all to ask important questions as well as understand the steps taken and explanations given as we went along.

does the thickness of the left ventricular posterior and septal wall gradually increase over time or it just happens?

In my case the entire left side of my heart increased over several years. My breathing continued to get worse and I was diagnosed with asthma. Inhalers, and nebulizers were prescribed to no avail. Then I experienced a sudden cardiac arrest. Mayo diagnosed me with HOCM. I had alcohol septal ablation, but I'm now I also have Cardiac Amyloidosis.
Having an echocardiogram is a must to confirm your HCM.

As @jachrist explained perfectly, it's gradual. The speed at which this happens varies as each of us is different. I was sorry to read that he needed to take the long journey before getting the proper diagnosis. That underlines the point that a cardiologist well-versed in HCM needs to be found to oversee your care. The problem for many is getting that proper diagnosis in the first place! To further explain the echocardiogram, it clearly shows where the HCM/HOCM is occurring and mine showed the increase in thickness yearly over time.