Tesla's system uses two wire transmission The ground is the second wire. The first wire in Teslas system was capacitive coupling thru the air. Transmission was directly 2 wire conductive as a huge spark, if the generated voltage was high enough to cause discharges thru the air.
In latter mythlike stories the ionosphere could act as the extension of that capacitor.
As an answer to your question: Transfer through the ground without another wire is possible in following ways:
send a low frequency radiowave through the earth; low frequency radiowaves attenuate slowly in the solid upper layers of the earth. No transmission to the other side of the world directly along the shortest path because the kernel of the earth is hot and that's why it is conductive which blocks the fields. If the transmitter antenna is sunken, then a global transmission can be(* possible - like shortwave communication is possible as reflections from the ionosphere. NOTE only the superpowers have a theoretical possiblity to fund thislike systems for global communication. The needed horizontal and vertical area for low frequency antennas is that huge. A "low cost" alternative is to sink it to the bottom of the sea and trying to use naval force to protect it against sabotage. NOTE: Quite impractical system for communication. Low frequency radiowave in the air has remarkably lower losses and it well enough penetrates through the seawater to reach the submarines. (But the questioner wanted it thru the earth.)
put two separate electrods into the soil. connect your source to them. Two separate electrodes far away can well catch a detectable amount of energy from the distribured current and voltage field. That catching principle was used as early as over 100 years ago as a way to secrectly listen telegraph and telephone signals on single wire + earth transmission systems
Use not electricity, but seismical thumps or have a nuclear reactor or a high energy particle accelerator that produces cosmic particles. For example neutrinos penetrate through nearly everything, only a specific possiblity to cause a rare nuclear reaction affects and make the neutrinos detectable.
*)only an assumption, not based on calculations or proven sources
Some explanations of Tesla's system for the interested:
No radiowaves thought here. Tesla claimed "This system is not derived from Hertz's. Actually he was right and wrong.
Wrong: he couldn't avoid radio waves to be born as a side product. They get the birth as soon as there exists suddent changes in E or H field intensities.
Right: The main effect was caused by fluctuating local, nonpropagating fields - or as a radio engineer says: caused by reactive nearfield. See the ADDENDUM!
In Tesla's experimental system the block "Supply of energy" was the spark gap output of a spark iductor. The transformer was connected to the ends of the spark gap thru a smallish capacitor (not drawn) to allow the sparks to develop without a short circuit.
Every time when a spark hits in "the energy source" the transformer gets a sharp impulse of several thousand volts.
Transformer is loosely connected - the coils had no common high permeability core, they stood only near enough. Thus the secondary coil of the transformer and the output terminals formed a reasonably high Q resonant LC circuit.
Output terminals (earth and the big "virtual ground terminal + its supply wire were a big open capcitor and all those amazing super high voltage effects in the air actually happened in the capcitor of the resonant circuit.
As said, the looseness of the transformed let the output side to have low resonant losses. The inputted sharp spikes have a substantial amount of energy in the resonant bandwidth of the output circuit. That causes the resonant AC voltage in the output circuit to gradually build up. It could easily be hundreds of thousands, even a million volts. That was noticeable even several meters away of the output terminals. But the AC fields stayed local and weakened as the distance was longer. That was not easy to notice in a room.
NOTE: The output AC voltage grew until discharges, the stream back to the supply and escaped radiowave energy were in balance with the total available input power.
Afterwards it is easy to think that having the output terminal in the ionosphere (at that era unknown), the output terminal could be global thus allowing a worlwide possiblity to catch the electricity by a long and high enough wire
But that's not true. The high intensity AC field could build up only if no remarkable losses existed. So-the power in the world wide electricity system would have been unavailable for use - as a wall socket that's not allowed to use.
Unipolar one wire transmission systems are constructed (even no earth is needed in the transmission job). Examples: Goubau line, metallic wavequide. But these systems must be considered as structures where a radiowave propagates quided by a single, maybe a long one piece of conducting material. Normally we use two wires as in twisted pair or coaxial cable. An analysis shows that metal and their surface current quides the radiowave that actually stays outside. In coaxial cable the radiowave propagates in the insulating layer between the conductors, but not inside the metal parts.
ADDENDUM: Vicious reactive nearfield surrounds radio transmitting antennas. Especially forceful it is when antenna is poorly designed and need a heavy tuning circuit to head the already back to the transmitter walking radiowave again to the antenna. Every radio amateur who has experienced with homemade HF antennas has smellt and felt his skin burning after touching some metal near that bad antenna.