No, you can't do this. A single LBA can process inputs of any possible finite length. For any individual input, there are only finitely many possible tape configurations but, over all possible inputs or all possible lengths, there are there are infinitely many possible tape configurations. A finite automaton can't have one state for each of these configurations.
In particular, LBAs can accept non-regular languages, such as $\{a^nb^n\mid n\geq 0\}$ so there are LBAs that can't be converted to a single DFA.
What you could do is produce an infinite family of DFAs, one for each possible input length. Each of these would have a finite number of states. However, such an infinite family could recognize any language – even undecidable ones! – because every language contains only finitely many strings of each length and every finite language is regular.