Questions about 浮かぶ and 永遠

Hello! I'm trying to translate passages out of my Hobonichi planner as often as possible, and I couldn't specifically understand the meaning of parts of todays quote.

Here's the full passage:

アイディアって、ほんとうに「一瞬」でパッと浮かぶものなんですよね。でも、それをかたちにすることは、「永遠」になるかもしれない。いろんなハードルや条件があつたりしながらも、たつた一瞬の偶然のようなひらめきから始めて、永遠に向かっていくっていうことが、ものを作るっていうことのいちばんの醍醐味だなと思って。

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And my translation is roughly:

An idea is really just a sudden fleeting moment, right? But by giving it form, it might become permanent. Despite the various hurdles and conditions, that brief moment of chance that sparks inspiration towards something permanent is, I think, the greatest pleasure of making things.

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In this context am I right that 永遠 means permanent vs eternal/eternity? And what exactly does パッと浮かぶもの meaning? Does パッと mean sudden? And doesn't 浮かぶ also mean sudden? Is this redundant or is there a nuance to this that I'm missing?

Any help would be greatly appreciated!

-Thomas

永遠 can have both meanings in Japanese.

浮かぶ means 頭/心に浮かぶ "to come to one's mind / pop into one's head / cross one's mind" there.

You seem to miss 始めて and 向かっていく part.

Ah I see, thank you!

Hmm... Could that third sentence be a bit more like "...when a sudden moment of inspiration begins, and you head to eternity / permanence..."?

It's not 始まって. 始めて is transitive.