How do I actively land my first B2B customer as a new business in the commercial office space industry?

1) First, selling something doesn't always have to be through testimonials or referrals. If your product -here commercial office space - makes sense, then, people will be interested. When I started my marketing agency, the first client I acquired was a big LED supplier in China and I did it by:
a)Giving a practical solution to his problem
b) Being professional at every front
c) Referring to my industry experience (not clients)

2) There are many things you can do to connect with potential clients in your local region. Here are a couple of them:
1) You can highly target ads in your region
2) You can create a killer office space introduction video
3) You can channelize your current network to get introductions

I think reading this B2B marketing blog I wrote couple of weeks ago will help you:
https://www.upreports.com/blog/marketing-growth-strategies-hacks/

Need further advice? I'm just a call away!

Rarely will any client care about testimonials. They only care about results.

Referrals, do your own.

Here's how...

Join https://Meetup.com networking groups in your local area + attend several each week. Be sure to attend the same Meetup groups at least 10+ times, so people get use to seeing you.

For groups with before meeting introductions, use something like this...

"If your office space is way to high for what you're getting + you can never get anything fixed, find me afterward. Likely I can help you..."

Then sit down.

Then stand 1/2 way up again + say.

"My name's {your first name here}."

Then sit back down.

Note: Keep refining your intro, using the above template, till clients start pouring in.

Share with your personal network, starting with family and your IRL friends when you see or communicate with them next, that you're looking for clients. They know you and actively want you to succeed and will be excited to give a great personal referral to someone they know who needs your services.