You can do it with a very high cost (in overhead, latency, and availability) by having a large number of people all send and receive messages, on a fixed or randomized schedule, exceeding their maximum possible amount of communication with one another. Then someone monitoring the network knows that each of the participants in this system could have communicated with any other participant, but not whether or not the communication took place.
The bottom line is that you are going to leave a signature of some sort through communications - the question is, can you properly build a comms system system that is functional within the limits of your risk/reward criteria.
To eliminate the statistical observability of metadata, the padding needs to reach or exceed the maximum capacity of the channel. So you can't have people sending more messages than the padded channel permits per time period. In your example, packets "with variable length/size content" would need to be absolutely prohibited, or else all packets' length would need to be randomized, and message data would need to be sent following strictly the same distribution as padding messages.
For example, you and I could have a rule of exchanging exactly 1 MB of data per day, at a specified time, every day. Then an observer wouldn't be able to tell whether, on a particular day, we had actually communicated something to each other or just allowed the padding data to go out. Clearly in this system we're not ever allowed to use it to transmit more than 1 MB per day, without destroying the metadata unobservability property. An attacker still knows that you and I are part of a system that offers us an otherwise unobservable channel, but not when we do or don't make use of that channel.
There are lots of variants that also allow many-to-many messaging, again at a high cost in overhead, latency, and availability.
You're also not ever allowed to transmit links or anything else that goads the user into fetching a remote resource in response to a message.
> For example, you and I could have a rule of exchanging exactly 1 MB of data per day, at a specified time, every day.
Depending on the size and popularity of the relay network, the fact the two parties are connected to it could be valuable metadata.
If you really wanted to minimize the amount of metadata to something that's almost useless, you'd probably need to use something like a continuously-operating broadcast numbers station.
My hunch is that it wouldn't be possible, and there would be a side-channel vulnerability somewhere.
Edit: the beginning of this research is the Dining Cryptographers.
https://en.wikipedia.org/wiki/Dining_cryptographers_problem
Although Chaum's solution has terrible availability properties, it's unconditionally secure against outsiders!
Importantly to how we think about communication, no.
Metadata is the signature that accompanies or encapsulates content, viewable to the world. You can completely conceal content, through encryption for example, but you can't completely conceal metadata.
In other words there must be a physical exchange of energy somewhere (communication), and metadata tells you something about how the exchange happened, irrespective and ignorant of what the content is.