If we register our startup name as a trademark, can we also get the domain name held by somebody else?

Hi, I would like to know about a trademark-related issue: We recently wanted to trademark our startup's name. There is no other trademark registered for that name. However, a company based in Brazil has registered the .COM domain with the same name and it doesn't look like the domain is for sale. If we registered a trademark for the company name, like STARTUPNAME (TM), could we do anything to get the STARTUPNAME.COM domain? Thanks!