Totally understand this problem, since we faced it very early on. I helped grow our travel community from 0 to over 70,000 travelers in less than a year and worked with JetBlue and Lufthansa Ventures at the accelerator that Dropbox and Paypal came from and this question came up over and over.
My best advice for you would be to create a brand around your business instead of competing with the Expedia's and Kayak's of the world for paid advertising space.
What this looks like in practice is essentially pivoting your social media strategy into a travel influencer brand that offers travel content to its audience and builds depth with the travel community. The difference between this and what someone like Kayak is doing is the following:
Paid advertising scenario:
Sally wants to fly. She goes to Google and types "flights to Houston". You can't outspend Kayak for this search. If your strategy depends on SEO or PPC, you're dead.
Sally wants to fly. She goes to the website of the famous YouTuber/Instagramer who has a travel app that she's always wanted to try out. She willingly consumes their travel content daily because it's fun, entertaining, and it makes her want to travel more.
You can only win on the branding scenario. It plays to your unfair advantages/disadvantages. You don't have money to compete with Expedia on PPC, but unlike Expedia, you as the CEO of the startup can curate or create content that is much more informal (memes, Q&A's, funny videos, travel bloggers) that gets you in front of your audience every day.
Happy to talk more about your business!