Can I get a seat at NIT Goa with 145 marks in the JEE Mains?

It is not mentioned in your question whether the home state of Goa is applicable for you or not. Not only this, the category from which you belong is also not mentioned in the question (General/OBC/SC/ST).

However, I would try my best to provide you with a suitable answer based on official data for the past few years, the total number of seats vacant, and the various departments available at the institution.

• You can easily get enrolled in a better NIT like many of the older ones.
• You can surely try to opt for other courses at the older NITs as it would be extremely beneficial for your career.
• I would suggest that you do not lose hope after the seventh round of counselling.
• There would be a special round to fill up vacant seats at the NITs and IIITs.
• For this round, you are required to submit a fee of INR 1,000 along with the online application form on the CSAB portal.
• Fill in your desired branch and colleges once more; vacant slots can be seen at the portal.

I am quite confident you'll receive the branch you want after the special round. You can refer to the cutoff details available on various websites to estimate the chances of your getting admission to one of the courses offered by the institution.