Congrats! You are very lucky receiving such fabulous expert advise. I wish we had founderdating by the time I was having my first experiences with that.
I have done every mistake in the book when it comes to working with Goliath. I'll share some of them below
Note: I assume differences between having interest from a Goliath and from usual investment rounds with private investors, VCs .etc
First mistake: Imagine / Act as if it's already done.
It's a great triumph feeling that after bootstrapping, we are being "recognized" by the big guys, also for the need to "qualify" your startup for the size of the deal, even subconsciously with positive expectations you start taking decisions as if the deal is already done, can be product, marketing or team decisions.
The morale of the team rises, you probably bring more, plan more product features and invest more in marketing to have a steep growth curve during negotiation.
In my case, as they deal was postponed and then cancelled. The morale of the team dropped, long standing team members left, the product/offering ended up with more features than we can handle and we prematurely launched a marketing campaign.
Until the dotted line is signed, hold your horses from any unplanned investments including the morale of the team.
Second Mistake: It's not about you, product/market expertise
As the startup CEO in the negotiation seat, we often assume that it's about "us", it's healthy to make it clear to you and your team that they are interested in the market your product is addressing.
It's good to assume that these guys developed interest in a market, evaluated existing products, studied building a product and either they had internal limitations/policy issues to execute or they thought they can reach a reasonable settlement with you.
Putting this in mind, will force you to focus more on their perspective of why they have this interest and most likely this will sustain their interest and help you close the deal as you maintain their initial thought that your product is the best fit.
Depending on the NDA you'll sign and their level of interest during the negotiation, if they can find a gap to go with other options after being offered your view and expertise in the market and product they'd go for it. I got $4.1 Million USD invested in a product I initially designed for a market I identified in a similar fashion by a Goliath.
Third Mistake: Your own time as CEO
As the CEO of the startup, you have your ongoing responsibilities to sustain and grow the startup, often big deals consume a lot of time, you might consider sharing some of your existing responsibilities with team members so you'd have more time to allocate to the deal or delegate this possibility to a team member CFO/COO beside hiring a consultant/advisor.
Might seem like novice advice, but it's very tricky.
Best of luck, I'm a big fan of startup/corporate deals and I hope this one works for you.