Put Up Placeholder Site ASAP or Wait for Full Site?

It can take some time for a new business website to get picked up by all the search engines and indexed.

Let's assume it's going to take a month to build your new full-fledged business website. Would it be advantageous in the mean time to immediately launch the domain with an introductory website using a template site so you might have just two pages, a home page with logo, title, brief description of pages, a couple images, etc and a contact page. Would this help give the site a "jump start" on being indexed?

Or could that do more harm than good by putting up something "quick & dirty" versus the complete website with much more content, that has been SEO optimized?

Getting indexed doesn't take that long if you give it a little hand
If the site will take a long way to build you can already make an "in construction" page with a brief blabla with your logo, main keywods, some content and a "leave your email here, we will let you know when it's ready" call to action to already begin to build your email list.

I would use your space by giving a summary of your ¨about me¨ page, a few testimonials if you have them and add an ¨email me when you go live¨. Gives a better overview of what you do and create anticipation for your product or service. Be sure to send a thank you email to everyone on your list. If you have any promo video such as Vimeo then password protect so you give your leads ¨Special Access¨. Make a 30 second YouTube promo video then I would embed then Rank through social media. Meantime, take Q&A through your Posts and address any issues and ideas for future content material.

I hope that gives you a few ideas.