You’ve picked a company from your list of persona-matching-companies, hurray 
now you research, read and dig through the company to find out how it works and why it works.
The goal here is to learn about the company, get ammo for when you reach out to know how to relate with them, what to focus on and what matters most to them.
Your task here would be to create a proposal, project, case study, or deliverable of some sorts that helps the company be better. It can either be a fix for something you see the company needs that is in line with your skill set, or a completely new deliverable that would be valuable for them.
When I wanted to work with a Fintech company, I did a research into the informal market and documented it via this article Enabling The Nigerian Informal Sector With Financial Services | by Osioke Itseuwa | Growth Clinic | Medium. It worked wonders for me.
Task: Create a deliverable your selected company will find valuable.
Quote the Task text and post your deliverable or details of it.
Next, you contact the company and do the do application.
Also, as an extra task,
Optional task: Note all you found about the company that you liked, loved or found interesting in a good way.
You’d need this for when you reach out to the company.