How do you go about creating a product marketing plan from scratch for an early stage start-up?

I think the first step is to understand your buyers and market, so you can define who you're targeting and how you want to position your product. So as you say, competitive research, understanding the pain points of your buyers and customers, talking to your sales team to understand why you win/lose deals and creating an outline of your target buyers (or personas, if you're into those!)

I'd then develop a GTM starategy, including defining where you want to position yourself in the market, and a messaging guide to outline how you want to describe the product, outline benefits, key differentiators etc. This also includes gathering any evidence you can such as customer testimonials. It's important to get aligned on this with all stakeholders incl. product and sales leaders.

From there, create a PMM roadmap of sorts, defining goals and intiatives depending on the needs of the business, what already exists and what needs to be prioritised. For example, if the company is focused on outbound sales, there might be a need to prioritise sales enablement activities. If it's very inbound, it might be improving the website, or increasing adoption. If the product hasn't launched yet, this will likely be working with product on their roadmap, developing a pricing strategy, and defining a plan for launch. Look for where PMM can add the most value.

Given that in early stage startups, PMM may be the only - or one of very few - marketers, this plan may need to be more of a 'marketing plan' than just a PMM plan. It really depends on the business model and stage, but hopefully that gives some ideas!