As per the policy, you can not transfer domain withing 60 days. You will need to wait for 60 days from the date of registration of domain while transferring it from one domain registrar to another.
As you would like to point your domain to new hosting provider' server, you can opt to nay of the below option -
1. Adding A record -
Contact your hosting provider and ask them to provide the A record for your domain. It will be IP address of your hosting provider's server. You can point it to your domain name so your website will run form your hosting provider's server though it has domain registration with other provider.
2. Update the nameservers -
You can update the nameservers too. Contact your hosting provider and ask them to provide the nameservers for your domain. When you will update the nameservers then your website will start working form their server.
Please note, in both case there will be downtime of 4 to 12 hours for DNS propagation.