How can I install Ubuntu on external SSD of laptop which has no internal HDD? It goes into a boot loop

My Acer laptop has a broken internal SATA connector on its motherboard and I am not able to get the BIOS detect any Internal Hard. But I have been able to boot Windows-To-Go from external SSD as well as running Ubuntu from live USB, both on Legacy bios only. I tried to Install Ubuntu from a Live USB on a 240 GB SSD I tried two different methods, Choosing option one to erase the drive.Then choosing "Something else" option. Both times the files are written but after reboot from the External SSD, I get a boot loop on black screen. After some research on Internet I see that the Ubuntu Installer needs to write to the boot record ( MBR) of the internal hard or leave its GRUB there. I do not have an internal Hard and it does not work. Can someone help me out here with clear instructions? Thank you!