Visa travel transform to independent travel?

A group of us secured visas to visit Japan for a 1 week hiking trip starting on Oct. 8 to Oct 15 . Does anybody know if we are allowed to stay in Japan beyond our 1 week tour since Japan will be open to independent travelers from Oct. 11, 2022?

Visa for a 1 week hiking trip starting on Oct. 8 to Oct 15 .
What you are likely to encounter is that on arrival into Japan, your seven day visa will set the duration of your stay, and that will be what is shown in your passport. You get seven days. Do not over-stay - you would not be legally in the country on the 16th.
In order to take advantage of the visa waiver program, you need the temporary visitor permit (it is not a visa), and that is the "sticker" so many people are used to. You will not have that.
It might be possibly to visit an immigration centre to obtain one, but you would want to confirm with them in advance the detail of what is required.

Thanks JapanCustomTours for your answer. Does it mean that if we received a 15 day visa from the Japanese Consulate for our 1 week trip, we can stay the full 15 days even though our itinerary was only for 1 week?

If you have a 15 day visa, then, yes, you should be able to stay 15 days - the immigration officer would probably note your last day as such in your passport. I have people coming for a one month trip and they secured a 90-day visa before the waiver program resumed, so they could have stayed three months if they wanted.
As an obscure note, your arrival day is day zero. That has been around for ages, but I did see an explicit reference to it again recently while checking something.

Thanks again JapanCustomTours for your answers. I really appreciate it.