This week he might be the only piece.
Olave could be one of the few playmakers left standing following the Saints' 22-14 loss to the Carolina Panthers last week. As the Saints (1-2) head into a game against the Minnesota Vikings (2-1) on Sunday (9:30 a.m. ET, NFL Network) in London at Tottenham Hotspur Stadium, they'll do so with injuries to wide receivers Michael Thomas, Jarvis Landry, Tre’Quan Smith and Deonte Harty, all of whom left Sunday's game early or did not play.
Quarterback Jameis Winston, running back Alvin Kamara and tight end Taysom Hill are also dealing with their own injuries, leaving Olave as one of the few healthy viable targets. Winston has struggled through back and ankle injuries, compiling 858 passing yards but also throwing five interceptions in addition to taking 11 sacks through three games.
If Thomas and Landry are out, the Vikings game will be the biggest test of Olave's short career because he won't benefit from the defensive attention Thomas and Landry draw.
When asked about the team's confidence on stepping up if they can't go, he said the Saints would be up to the task.
"I mean, having them would be a huge plus, but if they can't go, I feel like we're real confident in our group and our offense", Olave said. "We're just going to keep getting better, and if they can go, it's going to be a huge plus, but if they can't, we're going to make up for that."
So far, Olave has passed many of the initial tests. The 2022 first-rounder was one of the Saints' few offensive bright spots last week, catching nine passes for 147 yards in the loss to the Panthers. He's the first Saints rookie with a 100-yard receiving game since Smith did it against the Eagles in 2018.
But Olave wasn't exactly smiling in the wake of that Panthers game.
"I am a competitor, man, so when we don't win I don't really care about the numbers," Olave said. "I feel like we could get it going a lot earlier. We took a step forward, but I feel like there is a lot to clean up."
Olave's 268 receiving yards, which currently rank seventh in the NFL, is more than Thomas had through three games as a rookie in 2016. Thomas eventually ended up with 1,137 receiving yards that season.
It's not a surprise that Olave has been a solid addition. The No. 11 overall pick was linked to the Saints almost as soon as draft season began last spring.
The Saints were desperate for receiving help, and Olave seemed like a natural fit. It was part of an overhaul that included the return of Thomas from injury, the signing of Landry and the shift of Hill to full-time tight end from quarterback.
In a show of how much things have changed, Marquez Callaway, the No. 1 receiver last year with the absence of Thomas, has caught only one pass this season. Olave, Thomas and Landry all have double-digit receptions.
But it is a surprise that Olave has managed to rack up massive numbers while the offense has struggled to maintain any sort of consistency through three games. The Saints have done their best work in the fourth quarter, often while playing catch up, with 46% of their total yards coming then.
"I definitely feel like I've got a lot of room [for improvement]," Olave said following Wednesday's practice held outside of London. "I feel like I haven't played my best game yet. I feel like I can clean up a lot of things. I feel like, when I get targeted, I want to bring in every pass that's thrown my way, and I feel like I haven't done that so far. But I'm getting better every week and that's all that matters."
Olave currently leads the Saints with 17 receptions (but has yet to register his first receiving touchdown). His target share has jumped significantly from three targets in Week 1 to 26 in the last two games.
He's also been a favorite downfield target of Winston, despite mixed results. Olave's 18.2 air yards-per-target ranks third in the NFL, although some of those attempts have been desperation attempts in the fourth quarter, including two that were intercepted.
The Saints don't intend to stop throwing to Olave deep, especially if Harty -- who is little used this season but is one of the best deep threats -- remains out.
"Obviously, we have been able to hit him on some explosive plays down the field," coach Dennis Allen said. "I think that is a good thing. Certainly, we are going to continue to utilize him in that regard."
In Olave's final season at Ohio State last year, he was part of a trio of successful receivers next to Jaxon Smith-Njigba and Garrett Wilson, who was selected one spot ahead of Olave by the New York Jets.
Given the current injury situation, it's possible Olave could be put in a position to try to shoulder the receiving load of a struggling offense. If he succeeds, it'll certainly give an early boost to an Offensive Rookie of the Year campaign.
But for now, Olave and the Saints are just trying to figure out how to boost an offense that has essentially played only one complete quarter so far.
"I mean, we have been down these first three games. We all know we are going to fight," Olave said. "We are all competitors at the end of the day. We are not going to give up until there is no time on the clock. So, that is one thing I have come out with in these first three weeks. We believe in each other. We've just got to get that chemistry going and that rhythm going to be explosive the rest of the year."