Where can you find a Molten Core

You can use an axe or the multitool you start with to chop down trees, simply aim at the base of the tree and chop away.

bare in mind that some planets might not have trees or trees that produce wood (which is what you are experiencing). You could explore that planet a bit further to find trees or just jump to a different planet. A little bit of coal gathered from the surface will allow you to jump planets.

Some trees (which may not be present on every planet) yield plant fibre when cut down. Just use your matter manipulator.

Vines work as plant fibre. You can find those growing on cave ceilings. Cut them with the matter manipulator, too.

You can grow some yourself, which is renewable, but takes some time and requires some preparation. You'll need a few seeds (you start with those) and basic stone tools.