transfer data from my mac to time capsule without backup

What model is your Time Capsule (TC)? Look on the base if it is 2012 it will have A1409 on the label.

These are now 8 years old and the lifespan is over.. about double expected..

Since your Mac appears to be MBP with Catalina it has several issues with network connectivity to old TC that it matches with poorly. At the time the TC was released apple still used AFP protocol. They now prefer to use SMB3 which the TC does not support.

i have big date becouse my mac is full

Get a USB fast drive.. SSD would be best but a desktop type 3.5" drive will be ok. Get something big enough to do both a full backup and space to store files. Something in the 4-8TB range. You can partition it and use a cloner software.. Carbon Copy Cloner is one good one and create a bootable clone on the first partition.

Then offload some of the files on the Mac which are seldom used to a second partition.. but make sure you backup these files to TC.

If your TC dies.. very possible for 8 year old unit.. what happens to all the files you store on it?

If you cannot manage to get USB drive for the moment.. there might be some possible ways around the problem of slow speed to the TC but we need details of the network and how the TC is configured.

that mean if my tc dies i will lose my data !!! why

I am trying to understand what you are doing..

If you move files from the Mac to the TC and then the TC dies the files you copied to it are lost.

If you are merely copying files from the Mac which you have said is full then the Mac dies all your OTHER files are lost.. you have no backup.

You are in a difficult place using equipment unsuited to the task. That is why I recommended a USB drive to make both a backup and to move files off your Mac disk.. to give you some space.

And as protection to your files.

If you want to ignore the file loss issue and just copy the files.. by far the best method is to get ethernet thunderbolt dongle for your laptop and plug that into LAN of the TC. Ethernet is much faster than wifi on those old model TC.

If you are stuck using wifi .. are you copying files via the TC wifi? Or is the TC bridged to a faster router?

I need details to help speed things up since I have no idea how you are presently doing things.

Catalina as mentioned is not fast when copying files to older network devices like TC.

It will help if you give an actual speed of the copy.

Did you create a new folder on the TC to copy files to.. ?

I am assuming these are user files.. not system files which are extremely slow to copy due to being in use.

Download and install an App like Black Magic and run actual speed tests to the TC disk if you like.. that will give me some idea of the problem.

Are you connecting by wifi to the TC? What speed is the wifi.. Please check on both the computer and the TC.

Our normal expected speed is 60GB per hour so 3GB taking 7min is a bit longer than it should but if they are small files then not unexpected.

i got massage Not enough disk space to copy

Check free space in airport utility. How much is available?