I see two possibilities to do what you want. You can take a "template" installation how @Chad G suggested in his comment and you can do it all by hand. The former is easier the latter more flexible.
In addition to the suggestion from @Chad G I will explain some details. First download a Raspbian image. The smallest one Raspbian Lite is enough. Flash it to the SD Card and start it at least one time in your RasPi. This will do first bootup initialization and expand the root partition. Then put the SD Card back to the card reader on your management computer. That should have at least a linux operating system, better a debian derivate (debian itself, ubuntu etc.). Otherwise you will have problems to access the needed ext4 filesystem. I use a Debian Stretch installation. Look if you see the SD Card:
mngmt ~$ lsblk -po NAME,SIZE,RM,RO,FSTYPE,TYPE,LABEL,MOUNTPOINT
NAME SIZE RM RO FSTYPE TYPE LABEL MOUNTPOINT
/dev/sda 167,7G 0 0 disk
├─/dev/sda1 243M 0 0 ext2 part boot
├─/dev/sda2 1K 0 0 part
└─/dev/sda5 167,5G 0 0 LVM2_member part
/dev/sdb 3,7G 1 0 disk
├─/dev/sdb1 43,9M 1 0 vfat part boot
└─/dev/sdb2 1,7G 1 0 ext4 part rootfs
I find my 4 GB test card with
sdb*. Then mount its partitions and clean them up:
mngmt ~$ sudo -Es
mngmt ~# mkdir /mnt/sdb1
mngmt ~# mkdir /mnt/sdb2
mngmt ~# mount /dev/sdb1 /mnt/sdb1
mngmt ~# mount /dev/sdb2 /mnt/sdb2
mngmt ~# rm -r /mnt/sdb1/*
mngmt ~# rm -r /mnt/sdb2/*
Restore from tar archives. The
-C option depends on how the files in the archive are stored.
mngmt ~# tar -xf boot-partition.tar.gz -C /mnt/sdb1
mngmt ~# tar -xf root-partition.tar.gz -C /mnt/sdb2
Prepare settings for booting: change device names in
/mnt/sdb1/cmdline.txt and in
/mnt/sdb2/etc/fstab from PARTUUID=... to /dev/mmcblk0p. This is necessary because you use another SC Card with different PARTUUID. Depending on what is in the tar archive you may have to fix it by hand.
mngmt ~# sed -i 's/ root=PARTUUID=[a-z0-9]*-0/ root=\/dev\/mmcblk0p/' /mnt/sdb1/cmdline.txt
mngmt ~# sed -i 's/^PARTUUID=[a-z0-9]*-0/\/dev\/mmcblk0p/' /mnt/sdb2/etc/fstab
Deleting it and restoring it from the tar destroyed the special qualities of the "lost+found" folder in the root directory of the ext4 file system, so recreate it (there's no corresponding thing in the vfat file system):
mngmt ~# cd /mnt/sdb2
mngmt ~# rm -rf lost+found
mngmt ~# mklost+found
mngmt ~# cd
Then, it's time to umount the file systems so that all pending writes will happen and the flags for cleanness of the file systems will be set.
mngmt ~# umount /mnt/sdb1
mngmt ~# umount /mnt/sdb2
mngmt ~# exit
Put the SD Card into the RasPi and boot.
If you want to modify the partition sizes or to understand what's going on you can also prepare the SD Card by hand. Then you can follow this setup from Step 2: partition SD Card: Howto prepare a SD card from a tar archive.