We can't answer any of these questions without knowing where you live. Some places in the world have trains that go near national parks(or similar).

Generally a train that's rural enough to stop near national parks will have space for bikes.

Honestly, for most places in the states I believe you're pretty out of luck. The majority sentiment of this community is don't feel bad for using a car if it's the best tool for the job.

Generally there are few options unfortunately. This is probably the main thing that still ties me to my car.

To solve this we need to bring more nature to the city, and build out transit networks for popular outdoor destinations.

There is an Amtrak stop right by the west entrance of Glacier National Park. It is 2.5 mile walk from there to the Apgar Visitor Center, and from there you can get shuttles through the rest of the park.

I always just take a train there, if it's a place worth visiting they'll almost always have a train route passing by with a regular service throughout the day and evening.

For example if I want to visit the Peak District I just hop on a train to Edale and bam, I'm a 10 minutes walk from a bunch of different trails and things to see.

All the major national parks I've visited have been like this so far, if they didn't have good transport links how would they expect anybody to visit? And they want people to visit, to spend money in the local towns/villages that house those transport links, etc.

I'm within an easy biking distance to a national park! But this one is kinda cheating being in the middle of my city.

https://www.nps.gov/miss/index.htm

An electric gravel or mountain bike would be perfect. You can add bikepacking gear and some have options for extra batteries for longer adventures.

Renting a car, booking a cabin or yurt, or a resort if you're bougie

In Sydney were kinda lucky in that I can get on a very early train and head north, west or south and be at a national park within 1.25 to 2.5 hours to go for a day walk.

Here in Seattle we have Trailhead Direct. https://trailheaddirect.org/faq/

It's only active weekends and holidays but I know friends who have used it. A few disadvantages: you need to bring everything. All the water, for example. SO.... not my kind of camping, because I'm a lazy shit who's already humped too much shit and my knees are knackered lol.

I live in Southern California and I can bring my bike on the train to Lake Perris. It's only a 6 miles bike ride to the campground.

There's a website/app I really like using called Rome2Rio that gives you lots of options for getting from point A to point B. If there's a car-free way to do it, it'll typically show you.

In Canada there's https://parkbus.ca/ which serves some parks from major cities.

Do you live next door to one? If not then no. You might as well be asking "how to travel hundreds of miles to a place with no infrastructure without a car." It's unreasonable. You could cycle.

You could move to the middle of nowhere and ditch your car and then you can have nature 24/7 for free, no travel required. That's what I did.