Building backlinks to old domain before new domain (and website) launches.

Hey SEOs,

I've run into a new scenario and would love some help.

• Client currently has a website. Let's call it oldwebsite.com. It's simple and has no SEO work done to it.
• I'm building out a brand new website for them with (possibly) a new domain name. Let's call that one newwebsite.com.

Can I start building links to oldwebsite.com before newwebsite.com is live? I'll 301 redirect from oldwebsite.com to newwebsite.com. Anything else I should be concerned about?

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Thanks in advance