Very basic sudoku solver (will not succeed beyond basic sudokus)

Sudoku

import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

class Solution {

    static final int BOARD_LENGTH = 9;

    public static void main(String[] args) {
        /* Works
        char[][] board = new char[][] {
                {'5','3','.','.','7','.','.','.','.'},
                {'6','.','.','1','9','5','.','.','.'},
                {'.','9','8','.','.','.','.','6','.'},
                {'8','.','.','.','6','.','.','.','3'},
                {'4','.','.','8','.','3','.','.','1'},
                {'7','.','.','.','2','.','.','.','6'},
                {'.','6','.','.','.','.','2','8','.'},
                {'.','.','.','4','1','9','.','.','5'},
                {'.','.','.','.','8','.','.','7','9'}
        };*/
        /*
        exceeds time limit with
         */
        char[][] board = new char[][] {
                {'.','.','9','7','4','8','.','.','.'},
                {'7','.','.','.','.','.','.','.','.'},
                {'.','2','.','1','.','9','.','.','.'},
                {'.','.','7','.','.','.','2','4','.'},
                {'.','6','4','.','1','.','5','9','.'},
                {'.','9','8','.','.','.','3','.','.'},
                {'.','.','.','8','.','3','.','2','.'},
                {'.','.','.','.','.','.','.','.','6'},
                {'.','.','.','2','7','5','9','.','.'}
        };
        Solution s = new Solution();
        board = s.solveSudoku(board);
        for (int i = 0; i < BOARD_LENGTH; i++) {
            for (int j = 0; j < BOARD_LENGTH; j++) {
                System.out.print(board[i][j] + "  ");
            }
            System.out.print("\n");
        }
    }
    
    public char[][] solveSudoku(char[][] board) {
        while (!isGameFinished(board)) {
            for (int i = 0; i < BOARD_LENGTH; i++) {
                for (int j = 0; j < BOARD_LENGTH; j++) {
                    if (board[i][j] == '.') {
                        char characterAtThisCell = getCharAtThisCell(board, i, j);
                        if (characterAtThisCell != '.') {
                            board[i][j] = characterAtThisCell;
                        }
                    }
                }
            }
        }
        return board;
    }

    private Set<Integer> initialiseHashSet() {
        Set<Integer> allPossibleChars = new HashSet<>();
        allPossibleChars.add(1);
        allPossibleChars.add(2);
        allPossibleChars.add(3);
        allPossibleChars.add(4);
        allPossibleChars.add(5);
        allPossibleChars.add(6);
        allPossibleChars.add(7);
        allPossibleChars.add(8);
        allPossibleChars.add(9);
        return allPossibleChars;
    }

    private char getCharAtThisCell(char[][] board, int i, int j) {
        Set<Integer> allPossibleChars = initialiseHashSet();
        List<Character> numbersInBox = getNumbersInBox(board, i, j);
        List<Character> numbersInCol = getNumbersInCol(board, i);
        List<Character> numbersInRow = getNumbersInRow(board, j);
        remove(allPossibleChars, numbersInBox);
        remove(allPossibleChars, numbersInCol);
        remove(allPossibleChars, numbersInRow);
        if (allPossibleChars.size() == 1) {
            int onlyPossibleNumber = allPossibleChars.stream().findFirst().get();
            char c = Character.forDigit(onlyPossibleNumber, 10);
            return c;
        }
        return '.';
    }

    private List<Character> getNumbersInRow(char[][] board, int j) {
        List<Character> returned = new ArrayList<>();
        for (int i = 0; i < BOARD_LENGTH; i++) {
            if (board[i][j] != '.') {
                returned.add(board[i][j]);
            }
        }
        return returned;
    }

    private List<Character> getNumbersInCol(char[][] board, int i) {
        List<Character> returned = new ArrayList<>();
        for (int j = 0; j < BOARD_LENGTH; j++) {
            if (board[i][j] != '.') {
                returned.add(board[i][j]);
            }
        }
        return returned;
    }

    private List<Character> getNumbersInBox(char[][] board, int i, int j) {
        List<Character> returned = new ArrayList<>();
        int startI, endI, startJ, endJ;
        Boundary b = getBoundaryIndices(i);
        startI = b.boundaryStart;
        endI = b.boundaryEnd;
        Boundary bb = getBoundaryIndices(j);
        startJ = bb.boundaryStart;
        endJ = bb.boundaryEnd;

        for (int x = startI; x <= endI; x++) {
            for (int y = startJ; y <= endJ; y++) {
                if (board[x][y] != '.') {
                    returned.add(board[x][y]);
                }
            }
        }

        return returned;
    }

    private Boundary getBoundaryIndices(int number) {
        if (number < 3) {
            return new Boundary(0, 2);
        }
        if (number < 6) {
            return new Boundary(3, 5);
        }
        return new Boundary(6, 8);
    }

    private void remove(Set<Integer> allPossibleChars, List<Character> numbersToRemove) {
        for (Character character : numbersToRemove) {
            allPossibleChars.remove(Character.getNumericValue(character));
        }
    }

    private boolean isGameFinished(char[][] board) {
        for (char[] chars : board) {
            for (char aChar : chars) {
                if (aChar == '.') {
                    return false;
                }
            }
        }
        return true;
    }

    class Boundary {
        int boundaryStart;
        int boundaryEnd;
        public Boundary(int a, int b) {
            this.boundaryStart = a;
            this.boundaryEnd = b;
        }
    }
}