Is it possible to still claim my dependent even though I had no income last year, only child support/alimony

[xmasbaby0]

No.   If you did not have any income from working, filing a return claiming a dependent will not yield any sort of refund for you.  The child-related credits like earned income credit or the refundable additional child tax credit are based on having income from working.  If you did not work, you are not eligible for those credits.

[DoninGA]

No.  You must have at least $2,500 of earned income from work to be eligible for the child tax credit.  Child support is not reported on a tax return.

If you do not have any taxable income in 2023 then there is no need for you to file a 2023 tax return.