Although a common question, it is a difficult one to answer. The reality is that there is no way to figure out how long it would take for a site to rank on page one. It may never rank on page one. To determine your competitiveness for a page one position, you must consider what leads to to a ranking position.
First, a page's rank is all determined by Google's algorithm which includes over 200 factors, for example age of domain, length of content, amount of content, page specificity, amount of clean backlinks, and social signals. Each of these elements contribute to a page's position in the SERPs. Competitive sites will make sure to address each of these factors in their long-term SEO strategy. Are you adding new content regularly? Are you pursuing guest blogging? Is your content optimized with meta and title keywords?
The good news is that many sites in the therapy sphere are not aware of these ranking factors, nor do they have competitive sites in terms of SEO and online marketing. Thus, you can get yourself ahead of the pack simply with a site with a coherent architecture, pages that are optimized for specific key terms, and an engaging user interface.
Second, you must consider the geographic area in which you intend to rank. Ranking for "Anxiety Treatment" in a small town where you are the only therapist in town will be quite easy. On the other hand, if you are located in Manhattan and want to rank for "Anxiety Therapist", you better have a fully optimized site and a very aggressive SEO strategy that includes building credible links and driving traffic to your site through various traditional marketing methods. You will also need to be constantly updating your site through blogs, videos, etc. Even then, you may be hard-pressed to get on page one. There are no guarantees.
Last, you must also think about the specific term for which you'd like to rank. If it is something that nobody else is doing or trying to rank for, for example "underwater anxiety treatment" (I know, random), then you are much more likely to rank. There are probably only a few sites out there with content about underwater anxiety treatment, if any, so you have a much better chance of being in a page one position! Remember, find your niche and be unique. What is that one service that people are looking for that no one else can offer but you?
So, that is ranking in a nutshell. If you have further questions or would like to discuss your particular concern, please submit a ticket to contact Support.