What would be the best strategy for a small web design agency to have small companies as clients in the USA?

Niche down to help a certain kind of client.

Find out what serious problems you solve for them with your solutions.

Don't talk about SEO or web design: you'll turn yourself into a commodity if you do.

See this: https://www.jasonkanigan.org/what-to-do-if-you-are-a-commodity/

1) Start posting correct + useful SEO related content on your blog.

2) Arrange markup to be "Feature Snippet Friendly".

3) Buy traffic + run to various blog pages, especially your Feature Snippet checklist pages.

Facebook might be good traffic source + likely not good/profitable.

Best traffic sources to test - Outbrain + Taboola + Yahoo Gemini.

Please don't make the same mistake made by every other SEO / Web developer. As a small company ( your target customer) why should I have a web site? Don't laugh! What extra benefits I will get from my own website which I cant get from a free face book page or LinkedIn page?
Which is easier medium to reach , attract and retain my target customers?
Stop selling tasks or services. Start selling results. Go for a revenue share from the improved sales and have a 3 to 5 yr contract, with a provision to revise the share annually.
Don't go for volume driven discount. In fact pick up very small % in the beginning and increase the revenue share year on year based on the increased sales. This removes the entry barriers and gives you better returns in long term.
The challenge is that you cant offer the services to competing businesses. That becomes your unique selling proposition. You can actually ask the business to pitch to you so that you can better understand the revenue potential and work as a partner rather than a vendor.

There are three main new business strategies for agencies to create new business opportunities. As you are a service business you will sell on trust and capability. Rarely one or other. I would recommend a rounded approach to include all of the following networking, speaking, event/webinar, social selling strategic partnerships, fame through awards/pr and driving referrals from existing clients combined with an inbound content strategy. There is no one quick fix all approach to agency lead generation, don’t let anyone tell you there is! Good luck!

There are plenty of web design companies that give small business what they want—but not enough that will serve as a consultant and advise them on what they need.

If you have designed a website for a certain type of small business, and gotten them results, then start marketing to companies like them, talking results (i.e. sales), not just design issues. At the same time, don't turn down other types of small businesses that come to you. You want to build up your experience with many types of businesses, but the key is to specialize in your marketing.

First you have to define the niche you are targeting. Are you offering services to ecommerce? Auto dealership or?

You can do an initial outreach test by building a list of those targeted buyers using a solution like GrowthOK.com then I'll email those targeted buyers to see if they might be interested in your service. Make sure to follow up and sell well :)