You can add your GoDaddy domain in the service's Settings under Public Networking, then create the CNAME and TXT records GoDaddy shows you there at your GoDaddy DNS settings - both are required for traffic routing and ownership verification, and the certificate will issue automatically once they propagate (details at docs.railway.com/networking/domains).

I have already created the CNAME and TXT records GoDaddy shows me there at my GoDaddy DNS settings. I am still waiting for the railway dns propagation, may I know how long will it take to for the verification to be completed?

DNS changes can take up to 72 hours to propagate worldwide, though most propagate within a few hours, and certificate issuance typically completes within an hour after that. You can verify your records have propagated using dnschecker.org by checking that both the CNAME and TXT records resolve correctly.