fetch 10k records from 250k by searching from multiple indexed columns under 100ms

Question

create database task250;
use  task250;
CREATE TABLE Students (
    id INT PRIMARY KEY AUTO_INCREMENT,
    firstname VARCHAR(50),
    lastname VARCHAR(50),
    department VARCHAR(50)
);

CREATE TABLE Subjects (
    id INT PRIMARY KEY AUTO_INCREMENT,
    subject_name VARCHAR(100)
);

CREATE TABLE Marks (
    student_id INT,
    subject_id INT,
    marks DECIMAL(5, 2),  
    PRIMARY KEY (student_id, subject_id),
    FOREIGN KEY (student_id) REFERENCES Students(id),
    FOREIGN KEY (subject_id) REFERENCES Subjects(id)
);

CREATE INDEX idx_firstname ON Students(firstname); 
CREATE INDEX idx_subject_name ON Subjects(subject_name);
CREATE INDEX idx_department ON Students(department);
CREATE INDEX idx_firstname ON Students(firstname); 
CREATE INDEX idx_subject_name ON Subjects(subject_name);
CREATE INDEX idx_department ON Students(department);
SET @searchKey = 'Mana%';

SELECT * FROM (
    SELECT s.id, s.firstname, s.lastname, s.department, sub.subject_name, m.marks
    FROM Students s
    JOIN Marks m ON s.id = m.student_id
    JOIN Subjects sub ON m.subject_id = sub.id
    WHERE s.department LIKE @searchKey
    LIMIT 10000
) AS dept_results

UNION all

SELECT * FROM (
    SELECT s.id, s.firstname, s.lastname, s.department, sub.subject_name, m.marks
    FROM Students s
    JOIN Marks m ON s.id = m.student_id
    JOIN Subjects sub ON m.subject_id = sub.id
    WHERE s.firstname LIKE @searchKey
    LIMIT 10000
) AS name_results

UNION all

SELECT * FROM (
    SELECT s.id, s.firstname, s.lastname, s.department, sub.subject_name, m.marks
    FROM Students s
    JOIN Marks m ON s.id = m.student_id
    JOIN Subjects sub ON m.subject_id = sub.id
    WHERE sub.subject_name LIKE @searchKey
    LIMIT 1000
) AS subject_results

ORDER BY 
    CASE 
        WHEN firstname LIKE @searchKey THEN 1   -- Names starting with searchKey first
        WHEN firstname LIKE CONCAT('%', @searchKey, '%') THEN 2  -- Names containing searchKey anywhere next
        ELSE 3
    END,
    firstname 
LIMIT 10000;

I have 250k records in the database.

API response time acccording to different character searching lengths.

UNION runs three requests in parallel to save time.

How can I get fetch time on my local system under 100ms even for one character?