Gaussian signal generation circuit
There is an EDABOARD thread ( https://www.edaboard.com/threads/hardware-design-for-gaussian-filter.264943/ ) that discusses exactly what you want, a Gaussian filter implemented with opamps. The post https://www.edaboard.com/threads/hardware-design-for-gaussian-filter.264943/#post-1139855 goes into details showing &quot;a normalized 5th order Sallen Key filter&quot;. I attach a picture from this post to my answer:

The post warns on issue of practical usefulness of this design:

If gaussian filter is not perfect the data may not be corrected I think. Dont know how gaussian is used in real gsm

I.e., discussed is the Gaussian modulation as used in GSM (see https://www.etsi.org/deliver/etsi_en/300900_300999/300959/08.01.02_60/en_300959v080102p.pdf). This kind of modulation is called Gaussian Minimum Shift Keying (GMSK), and it modulates the phase of the wave.
Bluetooth uses Gaussian Frequency Shift Keying. GFSK uses a Gaussian filter for pulse shaping. The practical designs use FPGAs or CORDIC hardware to calculate digital Gaussian data. I do not know if the analog Gaussian filters are ever used in BLE designs.