Can a language be Turing complete without array support?

If a language has control structures and variables, but does not support arrays, lists, memory access and allocation, etc., can it be completed?

Perhaps if there was no limit to the number of variables that you can create, you can simulate arrays, creating a variable type array_1, array_2... array_6000and manually sort through them, and in some way to create complex data structures and recursion?

Edit: even if you cannot access the variables when manipulating names ( array_10+inot allowed)?

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