In most cases no, you do not need your own agreement with each airline before you can start selling flights on your portal. Flight content usually reaches a booking system through a supplier such as a consolidator, an aggregator or a global distribution system, and that supplier already holds the relationships and the ticketing authority with the airlines. Your portal connects to them, and their fares appear in your own search results under your own branding.
What you do need is an account with at least one such supplier in your market. That means signing an agreement with them, passing the checks they ask for, and agreeing how your bookings will be funded, usually a prepaid balance or a credit line they approve. They then issue the credentials your portal uses to search and to book. Until those credentials exist there is nothing for the portal to show, so it is worth starting that process early rather than leaving it to the end.
If you already hold your own fares with an airline, or you get special rates through a group or a consortium, those can often be shown next to the ordinary ones. Whether it works depends on the airline and on the supplier, because some fares are released only through one channel, and a direct connection to an airline normally needs that airline to approve you first. So not every fare you have on paper can always be sold online.
Before you commit, ask the supplier you have in mind which airlines they cover on the routes your customers really fly, whether budget carriers are included, and who issues the ticket. Those answers will show you how much airline paperwork is still yours to do.