The simplest way is just to test your prompts manually. You will also see how potential customers searchand what they normally see as results. At the next stage, you can add some AI visibility tools with a free plan in order not to waste resources and test you initial hypotises (such tools are Beamtrace, Mention Network, SEO for GPT). Or you can use cheap tools (same ones + new startups that I generally get from Reddit on r/saas and similar subs).
What I wouldn't do, is immediately subscribing to a costly tool: there are several large names with expensive pricings - they are probably fine, but it might take too much time to pay off your effort.