久しぶり and 初めて: a long gap and a first experience
Compare returning to a shop after a long gap with trying a dish for the first time, keeping the first experience tied to its object.
A long gap since an earlier experience
久しぶり, read ひさしぶり, means that a long time has passed since an earlier occurrence. 久しぶりにこの店に来ました。 says that the person came to this shop after a long gap.
久しぶりに友達に会いました。 says that the person met a friend after a long time. No exact number of years is specified.
The first time for a specified action or object
初めて, read はじめて, means for the first time. 初めて大阪へ行きました。 says that the person went to Osaka for the first time.
この料理を食べるのは初めてです。 says that eating this dish is a first experience. It does not refer to eating any food for the first time.
Different objects in the same situation
この料理を食べるのは初めてですが、この店には久しぶりに来ました。 says that eating this dish is a first experience, while the visit to this shop followed a long gap. The dish and the shop visit have different histories.
In 初めて大阪へ行きました。, the first experience is going to Osaka. It does not establish a lack of visits to other cities or a lack of any travel experience.
Does 初めて大阪へ行きました。 establish that this was the person’s first trip anywhere?
Show the answer and why
No. It says that the person went to Osaka for the first time. Earlier travel to other places is not discussed.