No, you are required to have obtained your Oman visa prior to your travel. 

Generally, the processing time for an Oman visa takes 4-7 days. However, you can also opt for express processing which takes 24-48 hours, urgent processing which takes 7-8 hours or super urgent processing which takes 3-4 hours. 

1) Visit Oman IE Visa
2) Select your living and citizenship country
3) Choose the visa type you require
4) Fill out the application form and upload the documents
5) Pay the visa fee
6) Track your visa status and download your visa.

Yes, you can choose express processing during the checkout. Super urgent processing gets your visa processed within 3-4 hours.