I might be in a 1% of engineers that believe in estimation. Can you make a step plan for some deliverable? No? Then, sorry, it's not that planning is not possible, it is that you are simply not experienced enough. That's fine. There is something called skills, and you can go get them. Have you made a plan? Great, then is there is some task in your plan that you can't estimate? In rare cases that might be inherently t…
I tend to disagree. Estimate this more complex situation: Integrate vendor B’s API where you don’t have prior experience with vendor B’s product let alone their API, and where our system is built specifically around vendor A’s API and workflow. This requires backend and frontend (customer and admin UI) changes given that everything is tied to vendor A’s API currently.
What are the key first steps? Investigate the API and product right? How long has that taken when you've done it before? Your first deliverable is a plan of it's that unknown.
Now you've investigated you know more about what needs to be done. You can compare it to previous times you've done similar things and estimate how long it should take.