Is someone able to tell me how to make this

You could possibly use scripts like this:

https://aescripts.com/after-ease/

https://aescripts.com/easy-bounce/

At the end of the day none of them are realyl necessary, though, and to boot they will only take a tiny bit of work off your shoulders. As is 90% of the time, the success in creating a convincing logo animation is just meticulous timing of keyframes and understanding animation techniques. The liquid writing itself is nothing too special. Just a bunch of strokes on paths with different delays, possibly "blobbified" a bit with blurs and Simple Choker plus some Roughen Edges to add irregularity. The rest is, again, just timing to make everything look weighty and splashy.

Mylenium

You can create liquid blends by combining Merge Paths and Offset Paths in a shape layer. Check this thread for some ideas and a sample project.

Recreating that animation will require interaction between a bunch of shape layers and the animated fluid brush stroke.  The hardest part to do without purchasing some 3rd party plugins will be creating the fluid brush stroke. 

What is your experience level with AE? That might help us point you to a solution.