If you're looking to create a script using the TypeScript Compiler API and leverage its type inference capabilities, it's actually quite simple.

To ensure your sample data can be compiled as TypeScript code, you'll need to structure it accordingly. The script will identify variable declarations and attempt to determine their types by analyzing variable and property names. If two objects share a property name, it will assign the type based on the first one encountered. Keep in mind that this may lead to issues if the types are different, which would require additional work to resolve. For JSON output purposes, your data sample could look like this:

File sample.ts

let raceCarDriver = {
    "id": 13,
    "name": "horst",
    "cars": [{
        "brand": "VW",
        "maxSpeed": 120,
        "isWastingGazoline": true,
    }]
};

The script has been tested with TypeScript 2.1 (recently released):

 npm i typescript
 npm i @types/node
 ./node_modules/.bin/tsc --lib es6 print-inferred-types.ts
 node print-inferred-types.js sample.ts

Output:

export interface RaceCarDriver {
    id: number;
    name: string;
    cars: Car[];
}
export interface Car {
    brand: string;
    maxSpeed: number;
    isWastingGazoline: boolean;
}

Here is the script: print-inferred-types.ts:

import * as ts from "typescript";

let fileName = process.argv[2];

function printInferredTypes(fileNames: string[], options: ts.CompilerOptions): void {
    let program = ts.createProgram(fileNames, options);
    let checker = program.getTypeChecker();

    let knownTypes: {[name: string]: boolean} = {};
    let pendingTypes: {name: string, symbol: ts.Symbol}[] = [];

    for (const sourceFile of program.getSourceFiles()) {
        if (sourceFile.fileName == fileName) {
            ts.forEachChild(sourceFile, visit);
        }
    }

    while (pendingTypes.length > 0) {
        let pendingType = pendingTypes.shift();
        printJsonType(pendingType.name, pendingType.symbol);
    }


    function visit(node: ts.Node) {
        if (node.kind == ts.SyntaxKind.VariableStatement) {
            (<ts.VariableStatement>node).declarationList.declarations.forEach(declaration => {
                if (declaration.name.kind == ts.SyntaxKind.Identifier) {
                    let identifier = <ts.Identifier>declaration.name;
                    let symbol = checker.getSymbolAtLocation(identifier);
                    if (symbol) {
                        let t = checker.getTypeOfSymbolAtLocation(symbol, identifier);
                        if (t && t.symbol) {
                            pendingTypes.push({name: identifier.text, symbol: t.symbol});
                        }
                    }
                }
            });
        }
    }

    function printJsonType(name: string, symbol: ts.Symbol) {
        if (symbol.members) {
            console.log(`export interface ${capitalize(name)} {`);
            Object.keys(symbol.members).forEach(k => {
                let member = symbol.members[k];
                let typeName = null;
                if (member.declarations[0]) {
                    let memberType = checker.getTypeOfSymbolAtLocation(member, member.declarations[0]);
                    if (memberType) {
                        typeName = getMemberTypeName(k, memberType);
                    }
                }
                if (!typeName) {
                    console.log(`// Sorry, could not get type name for ${k}!`);
                } else {
                    console.log(`    ${k}: ${typeName};`);
                }
            });
            console.log(`}`);
        }
    }

    function getMemberTypeName(memberName: string, memberType: ts.Type): string | null {
        if (memberType.flags == ts.TypeFlags.String) {
            return 'string';
        } else if (memberType.flags == ts.TypeFlags.Number) {
            return 'number';
        } else if (0 !== (memberType.flags & ts.TypeFlags.Boolean)) {
            return 'boolean';
        } else if (memberType.symbol) {
            if (memberType.symbol.name == 'Array' && (<ts.TypeReference>memberType).typeArguments) {
                let elementType = (<ts.TypeReference>memberType).typeArguments[0];
                if (elementType && elementType.symbol) {
                    let elementTypeName = capitalize(stripS(memberName));
                    if (!knownTypes[elementTypeName]) {
                        knownTypes[elementTypeName] = true;
                        pendingTypes.push({name: elementTypeName, symbol: elementType.symbol});
                    }
                    return `${elementTypeName}[]`;
                }
            } else if (memberType.symbol.name == '__object') {
                let typeName = capitalize(memberName);
                if (!knownTypes[typeName]) {
                    knownTypes[typeName] = true;
                    pendingTypes.push({name: typeName, symbol: memberType.symbol});
                }
                return typeName;
            } else {
                return null;
            }
        } else {
            return null;
        }
    }

    function capitalize(n: string) {
        return n.charAt(0).toUpperCase() + n.slice(1);
    }
    function stripS(n: string) {
        return n.endsWith('s') ? n.substring(0, n.length - 1) : n;
    }
}

printInferredTypes([fileName], {
    noEmitOnError: true, noImplicitAny: true,
    target: ts.ScriptTarget.ES5, module: ts.ModuleKind.CommonJS
});