Jesus talked about how the time he has physically with the Judean leaders is limited before Jesus returns to the Father. However, he did offer people a chance to come to Jesus.
First off, Jesus talks about how he gives thirsty people an offer to drink (7:37). By the way, the drink is figurative. The offer to drink implies a need to be replenished. If we're honest, we sometimes do not act good towards other people for no good reason, resulting in a not-so-good report as well as not-so-good side-effects, which include damage to our relationships. Thus, we have a need to be replenished and restored from our screw-ups we have made toward others -- and as we'll see later, the cross and resurrection that Jesus did fulfills the replenishment because Jesus clears us from our mistakes and demonstrates the power over death.
Additionally, Jesus talked about how when people believe in Jesus as per the Scriptures (note that Jesus is Son and sent by Father), their heart would outflow "rivers of living water" (7:38). This is also figurative, and John commented that the "rivers of living water" is a reference to the Holy Spirit that all believers receive (7:39). Before the sending of the Holy Spirit, Jesus will be glorified. As we'll see later, the glorification involves the resurrection after the crucifixion (death) on the cross. It's also worth noting that the phrasing of "rivers of living water" implies that the "thirst-fulfillment" is meant to last, and as seen in John 3, believers get a lasting gift of everlasting life (which involves us getting resurrected too).
Believing in Jesus is accepting that we need Lord Jesus (who is Son) to provide a way for us to "drink" and counting on Jesus for fulfilling the need to be filled for everlasting life (via the cross and resurrection). That's it for us. Jesus as Lord (and Son) gives us "rivers of living water" (via the Holy Spirit) and Jesus as Savior saves us from a scenario where we don't have everlasting life (via the sacrifice on the cross and resurrection).
For the readers who decided to accept Jesus and count on Him for saving us, you are guaranteed everlasting life. I don't have a "I raise my hand" button or "I accepted Jesus" button because faith starts internally. (You can raise your hand though.)