Help/Advice on making an M&A pitch for a boutique corporate finance firm

I wouldn't pitch an M&A idea at all for an IB internship, especially if the firm is focuses on advising on sellside transactions. You would be wasting your time. You just need a general understanding of what drives deals in the sector/region the boutique is focused on. 

First, you won't find financials for a private company beyond very high-level details like revenue, growth, and some profitability metric if you're very lucky. Financials aren't public if the company isn't publicly-traded. 

Second, IB recruiting isn't like hedge fund recruiting. In the latter, they ask for stock pitches because that's essentially what you do on the job. In IB, deals almost never come from a banker pitching an idea to a client, especially not a junior banker. Your pitch won't be taken seriously. 

When bankers pitch, it's because the company has said they want to sell or acquire in a certain industry/sector, so bankers in the "bakeoff" will show off their deal experience and potential connections with counterparties in the sector. You can have the greatest idea ever, but if you have no connection with either company nor its competitors, your idea won't be taken seriously. Not every company is up for sale, and you don't know unless you know the company management / shareholders personally.

Rather than a pitch, you need to just spend time learning the fundamentals of accounting, finance, and valuation and the classic behavioral questions. At the internship level, interviews will focus on those basic foundational questions (i.e., the M&I 400 investment banking questions guide). 

Fine to spend a day or so looking at the firm's transaction history to see who they advised and familiarize yourself with the general deal rationale for companies in that space. If the boutique is focused on a particular region or industry, the best thing to do is read up on those deals to see if there's any disclosure around financial / valuation details and trends in the space. 

Bankers do have a good sense of what trading multiples public competitors are trading at and the multiples that deals have gotten done at, so if the boutique's clients have all been private, look for competitors and precedents that are publicly-traded and study those.

Also see if you can identify high-level industry trends that are driving M&A in the sector or region of focus for the boutique. That in itself will make you stand out as a candidate if the boutique is industry focused.

It's extremely unlikely that an interviewer would ask you for an M&A pitch idea and expect anything beyond a 2-minute answer covering the high-level transaction rationale (unless you're talking through a deal listed on your resume). You volunteering a detailed pitch will be awkward and underappreciated. 

More commonly, you'll be asked things like, "Do you know the space we focus on? What is your impression?", "What are some trends driving M&A in this sector we focus on?", "Have you taken a look at any of the deals we advised on? What are your thoughts?"

For example, if the boutique you're looking at is a regional boutique doing deals of mom-and-pop shops providing various business services (e.g., janitorial services, HVAC, etc.) like many regional boutiques do...a good answer is something like:

"I've seen you guys advise on quite a few deals in the business services space. I think that's an area of the market where M&A makes a lot of sense currently. Oil prices are expected to surge from inflation, and it looks like the deals you've advised on involved consolidating acquirers doing bolt-on acquisitions to achieve synergies through route consolidation to minimize the cost of fuel. The public acquirers in the space seem to be trading at high multiples, and most have manageable levels of leverage. The industry still seems relatively fragmented, so right now seems like an exciting time for M&A in this space. That's part of why I'm interviewing here today!"