Your original sentence
This is grammatically incorrect:
You are missing particles between ポルトガル人 and 友達. You cannot describe the noun “友達” with “ポルトガル人” to make “Portuguese friend” without the の particle between the two nouns. This might be dropped in casual talk, but you still need to be aware of the particle being dropped. And 初めて is completely in the wrong place.
To say “the first XYZ” you would go 初めての XYZ. So here’s how you can break down your sentence.
I’m Yui’s first Portuguese friend.
I’m Yui’s friend: 私はゆいさんの友達です
I’m Yui’s Portuguese friend: 私はゆいさんのポルトガル人の友達です
I’m Yui’s first Portuguese friend: 私はゆいさんの初めてのポルトガル人の友達です
The Genki snippet by @alexbeldan just above my reply is the important thing to understand. Once you’ve made a noun phrase like 「ポルトガル人の友達」you consider that as just another noun when looking at the larger sentence. So now you have the “noun” for “Portuguese friend”. So to make “first Portuguese friend” you go: 「初めての(ポルトガル人の友達)」. And then finally to complete the thought as “Yui’s first Portuguese friend”: ゆいさんの(初めての(ポルトガル人の友達))です.
About 最初 and 初めて, I believe 初めて is more naturally used for the first time people “experience” something as compared to something like “the first shinkansen” where I would tend towards 最初の新幹線 instead. But I am not completely sure about this particular point. Maybe they can be freely interchanged. I’m just going off based on usage that I’ve seen.