How did Travelers bring matter/objects/artifacts into the past?

Like the other answer attempts to explain, The Travelers do not take any physical materials with them, but instead The Director is able to communicate with the traveler teams in the 21st Century either by sending coded messages on the dark web (mission statements), in other 21st Century devices (Ilsa), and/or sometimes from other established Travlers or new Travlers when they arrive.

The first mission ordered by the Director was proof of concept. Traveler 001 was sent into a host who worked in the World Trade Center on September 11, 2001, minutes before the attack. He was ordered to send a message indicating he had arrived safely, then die to prevent being traced. When the Traveler in question failed to send the message and escaped the building unscathed, the Director dedicated vast resources and personnel to tracking him - even killing two people via messenger just to order 001 to "self-terminate."

The Traveler program may have been put on hold in the future after the defection of 001. Simon - himself Traveler 004 - claims to have spent years searching for Vincent Ingram's voice. Simon's own mission from the Director was to set up the deep web communication network used by the Travelers.

The Teams then are able to "create" or "engineer" whatever physical materials they need per the instructions of The Director by using 21st Century material to make them, including advance medicines like nanite repair technology or quantum mechanic machines like the Quantum Frame.

It should be noted that "Historians" are often updated when the future begins to change and that "Archivist" are collecting information (through nanite encoded blood) of their experiences in the 21st Century back to the Director in the future, meaning communication goes both ways.

They don't. They go back to the past with them (or their Historian) knowing where to find the necessary materials to build whatever they need, with their future technological knowledge. The Travelers are sent back to the past by the Director overwriting the consciousness of the target person with the Traveler's, so they have no way of bringing back anything material.

They cannot bring any artifacts into the past. However, each team includes an Engineer, who knows how to make the artifacts using the 21st-century materials and technology, and a Historian, who knows where to get the materials.

An example of how they don’t bring it back in time:

If you recall episode U235, McLaren and his team had to leave uranium in present day so the director could get it in the future, then change the past from the future. It’s all a way of cheating for the director, kind of like in episode 17 minutes. They were overwritten because they were going to die, even though the only reason they were going to die was because of the director.
If you recall when Grace has to reprogram Marcy in the farm, they had to use modern day technologies, but they were able to apply it using futuristic methods/sciences. The reason for not advancing technology in advanced is most likely because it would change too many variables for the director to control/calculate, so they didn’t have mass production which makes it seem as though they brought everything from the future; because they had very little to keep undetected.