Ignoring that such bullishness is expected of the current administration's appointees, the devil's advocate can make a convincing case;
Q. Can NASA send a crew to the Lunar Surface by 2024? And safely return them to Earth?
Yes, they can.
Sandworm laid out the mission cost in lives problem, but modern spaceflight already has defined an acceptable margin for loss of crew in most missions - 1 in 270 as set by NASA for its Commercial Crew Transportation System (CCTS) program. The historical mortality rate for astronauts remains at 3.2%, or a Loss of Crew (LOC) rate of 4 in 125 across all vehicles and missions. Let us assume that the political calculus changes and the 3.2% LOC rate becomes acceptable. What's next?
What's next would be the design of a navigation system for translunar and cislunar navigation - after Apollo, and the exploration of the solar system, this has become a solved problem. We can run and code an AGC with inputs from far better sensors on an Arduino. NASA's engineers can also automate astrogation using Commercial Off-The-Shelf (COTS) technology. There are also highly efficient hydrogen upper stage engines available off the shelf for the Orion and the lander.
Unlike Apollo, 2020's NASA can use a more modern approach of Earth-Orbit Rendezvous (EOR) to construct the Trans-Lunar Injection (TLI) stage with a lander and lunar orbiter via separate launches. Low-Earth Orbit (LEO) rendezvous and docking has become routine for us in this era. It's a maneuver that's performed several times each year at the International Space Station. LIDAR and automated docking has made an EOR safe and, virtually, error-free.
For this theoretical exercize, the vehicle could be automatically assembled in an 100mi orbit. Crew could go up and rendezvous in the final lunar orbiter-and-return component of the vehicle, or in a temporary (Dragon) capsule. The EOR approach reduces the size of the launch vehicles required, making it feasible for a COTS provider like SpaceX to provide a Falcon Heavy for this purpose. It also allows for the re-use of current CCTS providers, by letting crew proceed to the vehicle in a human-space-flight rated Dragon capsule (or a mated CSM-equivalent). This system can be constructed via hardware that is currently being flight-rated, or will be flight rated soon, making the SLS redundant (in the short-term).
The SLS - for political reasons - could be repositioned as a long-term support and heavy payload delivery vehicle as a part of an extended Space Transport System, as originally envisioned for the Shuttle. SpaceX could provide the reusable "shuttle" aspect. The SLS heavy-lifter capabilities. And a lunar gateway as a refueling station. A deal that keeps all parties happy.
For the LEM component, NASA has the benefit of hindsight. The LEM designs still exist, there are LEMs in storage and can be mapped in 3D to study them. The data collected from 6 landings can be used to implement "in hindsight" improvements, making it easier to take the LEM template from Apollo and modernize it by reducing the electronics requirement and payload capacity. NASA doesn't have to redesign everything from scratch, there is a design that works. A design that was taken down to the surface with great uncertainty in 11 and 12, but worked for 14, 15, 16 and 17.
The most difficult aspect of the mission - the ascent stage - was studied following Apollo, and can now be trivially simulated in computer games, such as Kerbal Space Program. We can beg, borrow and steal the LEM design, and simulate what the original planners could not, giving NASA a much faster turn-around time this time around. It is conceivable that, if the payload characteristics were more realistic, and the goals of staying on the surface were trimmed down, a slightly up-scaled LEM and a down-scaled Altair/LSAM https://en.wikipedia.org/wiki/Altair_(spacecraft) could be made in 2 years or less. Flown in 3. Making it possible for an autonomous lunar landing in 4 and a surface jaunt in 4.5 years. However, that's theory, which would require tremendous resources to achieve.
After a cislunar docking maneuver, our astronauts can come home riding a far superior thermal protection systems than any contemporary material available in the Apollo-era. The amount of research that has gone into this area is extremely impressive, and gives our pioneers a safe journey home, where they'll land and descend via parachutes - which are far more complicated, but something that NASA, the organization, has more cultural experience with than SpaceX or Boeing.
From this template, a mission is not only conceivable - it's doable. The only question is how much.
How much is congress willing to give to make this a reality? And how far is the Trump administration willing to go to seal the deal?