The first computer to think about itself will also probably not be a 100% non-organic computer, but either a 100% Wetware computer, or more likely a hybrid. A wetware computer is a computer made with organic parts. There are efforts underway to create organic computer components, and they've made slow but non-zero progress.

Two companies working in this area are Cortical Labs [1], and Koniku [2]. I am associated with neither.

Two past efforts I've seen are a design for a computer using a fungal network [3], and organic neural networks in fabrics [4]. A lot of work on chaotic computer, such as organic computers, was pioneered by William Ditto, at Georgia Institute of Technology [5].

[1] https://corticallabs.com/

[2] https://koniku.com/

[3] https://royalsocietypublishing.org/doi/10.1098/rsfs.2018.002...

[4] https://www.science.org/doi/10.1126/sciadv.aba1178

[5] https://labs.sciences.ncsu.edu/appliedchaoslab/william-ditto...