1) Monitor Keyword Rankings
Initially every website will be targeted to few keywords which are relevant to respective website niche. SEO Professionals should make sure that "respective landing pages of the website should be indexed & ranked for targeted keywords". If your website is started ranking for few long tail keywords in the first month itself, it means "your SEO team is doing the right job". Also month over month keyword rankings positions should be improved. With the help of following kind of report everybody can measure their SEO effectiveness.
Note: This will not happen in all cases, because few of the niches are highly competitive, so it will take little more time to get results.
2) Analyze Monthly Visitors
Every website visits can be tracked through Google Analytics. It's free tool offered by Google, also simple to install & activate on website. Usually for a new website minimum two months' time required to receive traffic from search engines. From 3rd month onwards every website will start receiving little traffic and it should be gradually increased month over month. Of course, traffic increase in every month is a difficult task, so at least existing minimum traffic shouldn't be decreased.
If your SEO team is continuously adding new content pages then the traffic should be improved. So keep an eye on website traffic and measure your SEO team efforts. Ask your SEO team to provide monthly improvement stats and reports for your reference.