Is it possible to configure BIGIP with Node.js?

Porting from Python to Node is probably outside the scope of this forum, but the certificate management stuff should work fine. You have to do these things (in order, so you'll have to use synchronous calls or promises):

1- Upload the cert to a file on big-ip (using the api you already use)

2- Upload the key to a file on big-ip (using the api you already use)

3- Create a cert object from that file using this API: https://clouddocs.f5.com/api/icontrol-rest/APIRef_tm_sys_crypto_cert.html

4- Create a key object from that file using this API: https://clouddocs.f5.com/api/icontrol-rest/APIRef_tm_sys_crypto_key.html

5- Create a client-ssl profile that reference that key and cert object you made using this API: https://clouddocs.f5.com/api/icontrol-rest/APIRef_tm_ltm_profile_client-ssl.html

I'm not sure off the top of my head if the REST API saves the running configuration into the permanent configuration by itself or if you have to call the equivalent of "tmsh save sys config" afterwards to ensure it's saved. But it any case make sure your changes are persisted after running "tmsh load sys config".