Amount of water to boil (does it matter)

I'm in the midst of my first batch in about 8 years & have a quick question.
The kit I have is a full extract (pre-hopped) Irish Stout from brew craft. I've already done all my measurement conversions, since it's non-US measurements, but I'm boiling my full water amount (5 gallons) to help with the fact that I'm using tap water that most people in my area don't like.

The question: the directions call for boiling around one gallon & adding the extract to that, then topping off with the rest of the water at room temp and pitching the yeast. Will it make any difference at all if I add the extract to my 5 gallons boiling? I understand that I'll still need to allow the wort to cool substantially before pitching the yeast, I'm just more concerned about whether or not I need to dump water out of my brew pot & then re-add it once I get a boil going. It doesn't seem like it should matter in any way that I can think of, but I'm no expert...

Also - I am already aware that the batch should be 6 gallon, as it's non-US, I'm doing 5 on purpose.

Thanks in advance, the pot's only at 150 right now

Typically they say boil as much as you can, but this sounds like a hopped 'no boil' kit. Are you boiling the extract in the water for any length of time (e.g., an hour), or just adding the extract and taking it off the heat?

If the latter, then I think your main concern is cooling. If you boil the full amount, you won't have the top-off water to bring it down. You don't want to spend more than, I don't know, a 1/2 hour before pitching the yeast.

Also, boiling will take oxygen out of the water, and this works against the yeast. But even without aeration equipment, shaking the fermenter a bit can get some O2 into the wort.

It's not a timed boil at all. I don't believe it's to be boiled with the extrat at all. Pretty much just says to add to 2 liters of boiling water, next step add the balance of the water & then yeast (at 30celcius). I was just hoping to clear up the local water a bit by boiling it all, since I don't have filtered on hand & It seems a pain to dump most out just to add the kit & then dump it back

Edit: also thanks for the quick reply. It look like I should be fine I suppose.

This is a 'no boil' kit where the boiling is mainly just to sanitize the extract. Boiling your water will help if you don't trust your supply. You could have boiled some the day before, then allowed it to cool and used it as top-off water. But I'd say, just dump the extract in 5g of boiled water and then use an ice bath or something to bring the temps down before pitching yeast.